After 10 years there should be nothing in the coop that would hurt your chickens. That part would not bother me in the least. Personally I do not paint the inside of my coop, I just don't consider it necessary. But the most important part of a paint job is the preparation. Don't bother painting if you don't do a good job preparing it. That would be a waste.
After 10 years you will need to clean it to get rid of spider webs, dust, and such. A pressure washer is probably a good option but don't get the pressure so high you damage the building. That can happen.
I don't see a need to sterilize it but I don't see any harm in doing that either. When I sterilize things I generally use a weak bleach solution, let it set long enough to work, then rinse it off with water. Then let it ventilate if needed. Let it air dry. I don't know enough about other chemicals you can use to sterilize but I'd think with a little time they'd be safe.
Whenever I read a question like this I think back years ago to another thread. Someone was reusing a coop like you and found a group of small yellow eggs. Those were obviously not mite or lice eggs, nothing that would harm the chickens. The forum of course exploded with Clean! Clean! Clean! Kill! Kill! Kill!. I agreed that the coop needed to be cleaned but was also sad, thinking about how much fun the chickens would have had chasing down and eating whatever hatched from those eggs.