I had this worry when Harry had to be pts, I'd started a new job literally 2 weeks before and had the choice of going to Harry's appointment or being on time for a work meeting. The vet moved as much as possible to help but I knew I'd still be late.
All my worry was in vain, I decided to tell the truth, got there and my boss was lovely about it. Turns out he'd had rabbits when he was younger and understood- I'd never in a million years have expected him to react so well.
So perhaps just tell them the situation and see what happens- if nothing else they've got to respect the fact that you didn't phone in sick- good luck!