I would let everyone sit unless you have a friend you trust implicitly. It will take about two weeks for a decent rider to get the routine and rhythm with each horse. By that point you’ll be up on your feet — who are we kidding when we say we’re going to take the full “stall rest” before we get on a horse?
It never hurts to let them sit. It does hurt if your rider is not the right match.
I found a lease rider to ride my horse while I was out for ACL surgery and rehab. The rider I found was very well spoken of by connections I trust. She was supposed to work off rides in exchange for a free lease of a novice packer (she was getting into eventing from HJ land). It was a great deal for someone who wanted eventing exposure in exchange for an hour a week of chores.
Still. In that time, rider broke my $300 bridle by falling off of the horse I’d never once fallen off of in the eight years I owned him. She claimed he bucked. Some other very uncharacteristic things happened that I won’t go into detail over. I got my horse back with completely uninstalled buttons and broken tack.
The funny thing is, he was the first horse I rode post surgery… bareback and in a halter. Even though his lease rider was perfect on paper, it still was a mess. I would not do it again. I spent that whole summer after fixing some confidence issues he never had before I sent him out. And again — this was a lovely rider that came very highly spoken of from great connections.
Fingers crossed for your surgery.