In general, it's not advised to give a short clip or lion cut to a short haired cat. They need that layer of insulating fur to help them keep a stable body temperature. However, once the fur is badly matted, if your cat won't allow you to untangle it you have limited options. Mats aren't an immediate risk, but they can grow to the point they start pulling on the skin, causing pain and eventually sores and infection.
First option: Talk to his vet about giving/increasing pain relief. When a cat just gives up on grooming, it's often a sign of significant pain. If your cat isn't on anything for his arthritis yet, it might be time. If he feels better, he may start cleaning himself again, which should help, although you will probably have to help him with the worst of it.
Second option: Home remedies and enormous patience. You can use a cat hair detangler spray from the pet store, or little bit of a safe, edible oil (like coconut or olive). Don't overdo this, since it can get messy, and if you cat licks up a lot of oil it can act as a laxative. Apply sparingly to the mats and let it sit for a while, then try to tease out the mats with a wide tooth comb or dematting rake. If you choose to use a rake or razor comb, follow instructions carefully or even look for a youtube video of how to use it.
You will probably need to train him to allow grooming. Start very small. Give lots of treats and praise; start by praising and treating him for just letting a brush come near him, then accepting even one gentle stroke of a bush, etc. You should aim to work on the mats just a few minutes at a time, a few times a day until the problem is resolved. Try to make this process as pleasant and rewarding as possible for your cat.
Third option: Find a vet or groomer who can clip just the matted areas without sedation. Your cat may have 'bad haircut' for a while, but the stress is less by clipping just the mats compared to a full lion cut.
I don't recommend trying to cut mats with scissors! There is too much risk of hurting your cat, and it doesn't work all that well, either.
Final step: Maintain your progress with regular brushing. A slicker brush with soft-tipped bristles works well for most short coated cats, or if he's a fan of petting but not the brush, try a grooming glove.