I can't tell you what's involved with a complete knee replacement but with an ACL reconstruction, I had to get a letter from my surgeon outlining what was performed and that I was fit to return to pre op duties, a letter from my physio and then when I went to the FAA doc, I had to prove I had both strength and balance back in the leg. She submitted all he paperwork to OKC and they all they said was that if I had any issues relating to the surgery, that I had to inform them.
As far as the flying is concerned, initial V1 cuts were interesting. Look up proprioception. Amazing how quickly the body can forget simple tasks but then relearn them.
Got my class 1 about 3 months after the surgery.
Good luck.