As a heads up, EDMC runs natively on Linux well, or at least it did the last time I used it. See https://github.com/EDCD/EDMarketConnector/wiki/Installation-&-Setup#linux-with-steam-play
Since you’ve got it running in wine just fine, I personally wouldn’t change anything, but if you have issues in the future, you can try that.
You can tell git to use a specific key for each repo. I have the same situation as you and this is how I handle it.
https://superuser.com/questions/232373/how-to-tell-git-which-private-key-to-use