I've never dealt with arthritis, but I have been forced to work around sore body parts related to joint and soft tissue problems.
Joe DeFranco's recuperative shoulder routine has appeared in quite a few places over the last several years with almost 100% positive feedback. Because it is a circuit routine, you don't have to use much weight at all.
Here is a link: https://www.t-nation.com/training/shoulder-shocker
Joe provides an excellent demonstration video further down the page.
He also advocates regularly doing band pull-aparts to promote general shoulder health. Personally, I prefer doing this movement as a reverse fly on a pec-deck for the even/consistent tension it provides over band work. However, bands afford you the ability to perform a quick set anytime, anywhere throughout the day.
I hope at least some of this information can help you a bit.