How should I groom my cat?

Call a groomer and ask . My cats are all short hair and one medium hair so I've never tried but I understand where you are coming from. The worst they can do is shave it to short and he will look silly for a bit and only you will see him. They by the time the fur grows back all the way hopefully the weather will be not as hot and the shedding will stop. It's worth a phone call at least