Screaming is not good. If your cat is not declawed (which is bad bc it's inhumane) it would be wise to trim their claws... just take the tips off about 1/8 inch. Front and rear. After a few times your kitty will get used to having it done and will tolerate it being done.
I have 3 kitties... two of which are bigger than my Yorkies (a 10 DSH, a 12 lb Himmy, a 22 lb Bengal). I have a cat tree for the cats to be able to get up and away from the dogs if need be. Most times the cats prefer to play with each other and the dogs play with the other dogs but occassionally intermingle, usually involving sneak attacks by the cats!