I was wondering the same thing, but only found vet dental cleanings online in regard to diabetic dental care. In a “normal” cat, vets will recommend brushing their teeth, but I looked at the ingredients in the most popular feline meat flavored toothpaste and it contains dextrose, which is sugar, and sorbitol, which is a carb and also raises sugar some. Not sure why that would be in toothpaste other than to make it palatable, but I would not think anyone wants to give a diabetic cat sugar.
May be worth asking your vet what they normally recommend and see if it makes sense.
I was thinking of brushing without toothpaste, very lightly just to remove the food left after eating. They have very tiny cat tooth brushes or you can take a soft damp cloth, like the corner of a thin, clean dish towel or washcloth wrapped on the end of a finger and gently pass over the outside edge on both sides, this may be less invasive, I do know most food gets lodged on the outside of their teeth. I would not be too aggressive with this and only do if they do not have existing dental issues, trying to do this on a cat with inflamed or hurting gums/ teeth may only be hurting them and pushing bacteria into their bloodstream. If their mouth is in good shape and/or well healed after a dental, that may be the time to start and keep it up. The other issue is many cats won’t like you trying to get in their mouth (hmmm, it’s a cat). I tried to start brushing my cat’s teeth after her last dental. She hadn’t had her teeth cleaned in several years and I wanted to take care of her mouth after the cleaning, but she would not let me clean her teeth. I probably gave up too easy and figured I would just keep up with vet cleanings now, but the diabetes is now complicating that plan. I am thinking of trying again with a soft cloth and just rub lightly on outside of cheek/chin like being petted with damp cloth and talk soft to her to get used to the idea and see if she is vey relaxed would allow me to eventually, lightly pass over outside edges of teeth. I imagine it would be similar in training the cat to accept blood testing, just patience and not stressing the cat. Again, check with your vet.
In regard to your concern with putting them under, I sympathize. I did look online and there are some vets that have written articles on their methods, ie adjusting / skipping dosing, feeding / not feeding before and carefully monitoring them during procedure. This of course should all be standard, but you learned the hard way things don’t always turn out the way they are supposed to.
Here is an article I found from a vet that seems to be overly cautious with his diabetic patients and knowledgable about their care during dentals. Maybe interview and research vets in your area and find out their methods for procedures on diabetic kitties if you are not comfortable with your current vet on this. That is what I am going to do now even though I have been going to my vet for 20 years. After hearing stories here, we can’t always blindly follow what our vets tell us. Trust but verify.
https://www.adwdiabetes.com/articles/dental-cleaning-diabetic-pets-ask-dr-joi