It's actually advised for safe sleeping for Dad/Partner who hasn't given birth to be on babies side so they'll physically have to pick up and put baby back in the crib after Mum has fed (and make sure Mum hasn't fallen asleep). Lots of couples practise this anyway, even without your circumstances x
No guilt! We did the exact same thing for about 6-7 weeks until I was able to get in and out of bed without any strain. I also think it helped my husband feel more involved/helpful in the feeding process.
Whenever I feel mum guilt I tell myself “it’s really not that deep” Baby is okay and you’ve figured out a good system so don’t stress too much and just focus on recovering so you can be in the best shape (mentally and physically) to continue looking after baby