You may be able to use electric clippers; I've partially shaved 4 cats. All who got their first clip as adults. Clippers work best on mats that cover an extended area such as the whole way up a leg. It is still possible to damage the cat's skin with clippers. Take care doing the top front of the leg. my cat is not playing ball but I've tried to point where. There's a thin fold of skin that can fit between the teeth and easily be cut. I've also grazed a cat using clippers but I'm not 100% sure how.
You will almost certainly need a friend to hold the cat so you can access & see the mats. I recommend you do it in the bathroom, sat on the floor, as they are a small space and with the cupboards closed are lacking in hiding spaces.
The easiest one to clip was the semi feral medium coat. Matted chest/ belly, armpits and back of leg. Under the circumstances I had to do it alone.
1 get everything you need in the room first. Comb, clippers, extension cord. If you are using a power point outside the room make sure it is turned on.
2 remove a mat and then let the cat go or pat/stroke them for a bit
3 if the cat really is not happy get a professional to do it
4 don't use clippers on a cat's head.
Once I had the first few mats off Kasie was willing to lie on my legs.
The most difficult cat to clip was my friends Maine Coon cross who is super cuddly but complains and twists every time I try to scissor him.
Remember to brush/comb your cat daily after you have removed the mats to prevent new ones.