I think she will continue to trust you as she probably won't associate the op etc with you ...

Give her plenty of treats etc to keep her sweet

I had to get my stray cat spayed last week and was able to borrow a cat trap from local cat charity to get her to the vet , it might be worth a try doing the same if you can source one.
Basically once the cat gets into the trap , which is a big cage, you throw a blanket over the cage , the cat thinks they're in a cave and it completely calms them . My cat spent a night at the vets and the next 24 hours in our shed in her cage (she's also an outside cat). I checked on her every hour or so and fed her and gave her water and she was fine - I kept the blanket over the cage though , it really does keep the cat calm.
When I let her out of the cage , I had some sardines ready for her and she was delighted !!

Good luck and good on you for taking care of her