When I went through rush way back in the day, we were never offered food so it wasn't an issue -- so take what I say with a grain of salt. I don't think you'd have to offer an explanation as to why you're turning down food -- isn't it enough to say "No thank you" -- I mean, maybe it's not and I don't know where you're rushing, but I would never be offended by that. I would think it's enough to decline food and maybe accept a drink and be done with it.
Also, please don't feel the need to dismiss being vegan as silly. I really admire that -- I've been a vegetarian for over 10 years and I have mad respect for you for being vegan.
Good luck!!