Besides the below, I want to call my vet and ask 1) whether they do cat shaves without sedation, and 2) if they have any advice in terms of referrals or day-of care or whatnot. (they're open Tue-Sat)
They never do cat shaving / grooming without sedation. They recommend you first try one or more groomers, and if there's real problems with aggression or whatnot, then at that point they might recommend having them do it (but only with sedation).
Sometimes a groomer needs to send the cat home, and do it another day.
She recommended me to contact Countryside Vet Center, 708-469-6050. (open every day of the week)
If I have bad experience, then call back to Clippin' Critters and let her know. (if it's a good experience, then there's no need)
Cat grooming is much riskier due to their thin skin. Also, a lot of groomers just don't offer that service because the market prices mean that it's just not worth it. And cat temperament can be harder to deal with than dogs.
TODO
Check my local vet.
Don't look at Petco or PetSmart.