T/C has two platforms (frames) one is the G2 and older contender and the second is the encore.
The G2 can not take they higher pressure rounds the encore can take most but not all the higher pressure rounds.
All the contender/ g2 barrels are interchangeable with a very few exceptions, all the encore barrels are interchangeable, but you can not put a contender barrel on an encore frame and you can not put an encore barrel on a contender frame.
The 243 you are talking about must be put on an encore platform.
If your frame is listed as a long gun then leave it that way. it is best to play it safe. it is true that there is no case of a person being convicted of putting a handgun barrel on a long gun frame, and I doubt that a game warden or LEO would take the time to check if everything else was on the up and up. but I don't want to be the test case for that? do you?
One last thing before you go out and buy a handgun barrel and hunt with it, check your state, county, town and even property to see what the regs are, the regs can change from town to town and even some public lands wont let you hunt with a handgun.