What are your favorite games that can be played one handed?

Sorry to hear about your hand. Hope is mends quickly.
Many puzzle games need only mouse and can be very challenging and immersive. SpaceChem would probably keep you busy. Pony Island is a pretty unique experience and had a great story and dark humor - pretty sure you can play that one with just a mouse and/or arrow keys. The Cat Lady is a point and click - also a very good story, if you don't mind dark.

A dungeon crawler seems appropriate
https://store.steampowered.com/app/207170/Legend_of_Grimrock/
https://store.steampowered.com/app/251730/Legend_of_Grimrock_2/
https://store.steampowered.com/app/317370/The_Keep/

or this kind of game
https://store.steampowered.com/app/663380/Tales_from_Candlekeep_Tomb_of_Annihilation/
https://store.steampowered.com/app/317820/Guild_of_Dungeoneering/

or puzzle game
https://store.steampowered.com/app/288160/The_Room/
https://store.steampowered.com/app/425580/The_Room_Two/
https://store.steampowered.com/app/456750/The_Room_Three/

I hope you'll be fine soon.

There are TONS of turn based strategy games that are playable using only mouse, ( I am lazy and like resting my head on a raised arm), isometric rpgs are also an amazing choice. Many turn based strategy games allow you to drag or rotate the map with right mouse button if needed. City building, card deck based, and puzzle games are also good mouse-only.

ISLANDERS / Hexcells / Mini Metro / Morphblade
Opus Magnum / Bridge Constructor type games / World of Goo / Train Valley / Turmoil
Frostpunk / This War of Mine / Sheltered / SKYHILL
Slay the Spire / Darkest Dungeon
Divinity Original Sin / Pillars of Eternity / Omerta / Massive Chalice / etc
Civilization series / Stellaris / Tropico series / Cities Skylines

And, if someone didn't already tell it, I should say : Most of the Point & Click games, using a mouse ?

...Otherwise, my first "real" one-handed game using gamepad I remember so far was Ys I, on the Sega Master System, especially because you only have to "bump" into ennemies from a certain side in order to harm them, unlike the other "classic" Zelda-like games.
The remake still worth to be played this way : https://store.steampowered.com/app/223810/Ys_I__II_Chronicles/

Battle for Wesnoth! On Steam, too!

Where is Deep space waifu?
( ͡° ͜ʖ ͡°)

Also SIMS series :)

Hexcells, Squarecells, and Crosscells

Wish you well recovery ;)

You could try rally games if you're interested. Any Dirt game or Grid series. Reconfigure controls to have gas/brake near steering and its good.
No need for handbrake - use scandinavian flick

btw I've recently really enjoyed Project Highrise. You can play it with mouse only

Chroma Squad is pretty neat and only requires a mouse. Plus, you already own it.

I had an issue a few years ago where I couldn't use one hand. Any turn based RPGs will be good and tower defense games can be played (just not to perfection)

Most Strategy and tactical-RPG games. There are also logic/puzzle games.
Cards games and most Tower Defense games works too. There are many options ;)

And one suggestion: Desktop Dungeons (puzzle/tactical/rogue-like)

I really loved the 2 Orwell games, Limbo, Inside, a normal lost phone, another lost phone (Laura's story), Her story, Grim Fandango, the Deponia series, Kingdom: new lands, this war of mine and a coop game, Keep talking and nobody explodes. Also considering how popular it is, maybe there's a mod for Undertale to play it with the mouse? And as someone stated before me, most RPG maker games can be played one-handed, so all Freebird games + Rakuen :)

Papers Please https://store.steampowered.com/app/239030/Papers_Please/
Civ 5 https://store.steampowered.com/app/8930/Sid_Meiers_Civilization_V/
XCom: Enemy Unknown https://store.steampowered.com/app/200510/XCOM_Enemy_Unknown/
Don't Starve https://store.steampowered.com/app/219740/Dont_Starve/

Tore my right rotator cuff a while back, had to keep my arm in a sling, no use of my main hand. Switched my gaming mouse around to use left handed, and used, of all things, Windows 7 Accessibility inputs (Speech Recognition) to control keyboard with voice input.Works well with some games, not so well with others, and did take some work to get things set up. There are also voice command programs like Voice Bot https://store.steampowered.com/app/374400/VoiceBot/ , Voice Attack https://voiceattack.com/Default.aspx#download-1 and others (some free on the Web) to allow you to control your PC with voice. You do need a headset with a good mic.

Article here by a site that rates games and programs for people with disabilities: http://www.caniplaythat.com/2018/12/23/using-voice-recognition-to-play-video-games/ (applicable since you have a temporary disability...)

I was able to set up and play Grim Dawn and The Long Dark (2 of my favorite games) to work with Speech Recognition SW, though it did take some time to set up and get used to. But, it is a good option, if you have lots of time (and patience) to spare, and have games that are m/kb games that aren't piano player games (requiring rapid continuous key presses... aRPG's like Grim Dawn or titan Quest will work, but not if your build requires you to spam 6-8 skills and switch loadouts rapidly).

Best of luck to you, and sorry about your hand. I hope it heals quickly without lasting pain afterward.

https://store.steampowered.com/app/457140/Oxygen_Not_Included/

https://store.steampowered.com/app/221260/Little_Inferno/

https://store.steampowered.com/app/8930/Sid_Meiers_Civilization_V/

Wish you recover well. These are mostly strategy games but can be played only with a mouse. Pillars of Eternity could be irritating without a keyboard but still can be played with a mouse. Others will be fine. :)

100% Orange Juice
Age of Empires II HD
Civilization V
Cossacks 3
Anno 1404 aka Dawn of Discovery
Europa Universalis IV
Long Live The Queen
Might and Magic Heroes III
Papers, Please
Pillars of Eternity
Prison Architect
Stronghold Crusader HD

Basically any turn based strategy/rpg.

Most has probably been mentioned already, but... turned-based games (Heroes of Might & Magic, Civilization, Worms - though that one might me a bit harder) are certainly what I'd spend my time with in your situation. Other than that, games like Darkest Dungeon, Prison Architect, Game Dev Tycoon, This War of Mine, Race the Sun, Hearthstone, Business Tour (if you can play with friends), Papers, Please, + maybe some racing games (with automatic transmission of course). Not sure about these, but I also think South Park: The Stick of Truth and the Shadowrun series should be playable with one hand?

Anyway, hope you get well soon enough :)

Dota Underlords! It's free. It can get quite addicting if you get into it.

Tropico 4 is great. Best campaign mode in the series.

Sorry to hear about your hand. My initial thought upon reading the title was visual novels, especially those with fan service. Classic single handed stuff. :) But not really appropriate for your situation.

Really, I'm not playing much these days and I'm not sure what to offer that hasn't been suggested. I do play some the Oculus Go, and that's controlled with a single hand. Would be a little harder to put it on with one hand, but I just tried it an it's definitely possible and would probably become second nature with some practice. So if you're willing to spend about $200 on a Go to experience some basic VR, all control is single handed.

Ouch, that sounds terrible – wish you a speedy recovery.
Looking at your library, I'd suggest Fez. I don't normally like platformers or pixel art, but Fez has unique qualities that make it transcend its genre.
The Civilization franchise will also make those four weeks seem like four days....

Defense Grid: The Awakening

View attached image.

Any of the LEGO games. I always map every control except for camera movement to one hand, and since these games are slow-paced, when I do occasionally need to rotate the camera, I can just move my hand.

get well soon man

Maybe some RTS games could be ok?
yes they use KB for shortcuts etc... but you should be able to play them with mouse only...