Could i remove the cat converters that are shot and put this type of exhaust system in place of them?
Catback exhaust systems attach to the outport of the catalytic converter. So if you buy a catback exhaust system, that means the cat is not included.
Cat-backs are ready to go systems for a specific application. They attach behind the catalytic the flange by 2-3-or 4 bolts. This would not be the way to go in your problem as it is from the cat rearwards. Best bet is to go to a parts store and get a generic replacement. Since you didn't list a make or model, it could be possible to eliminate the cat if it is pre 95 or without OBD2. This is NOT a LEGAL fix in any state, however. Wink-wink! Recommend replacement with a high flow cat.
It's just like it sounds, it's the exhaust system from the cats back and not including the cats.