It will more than likely have to be fitted to the gun, John. My experience is the Remington model 17s about nine out of ten times, the barrel will interchange between guns. The pre 855,000 Ithaca 37s almost never interchange. A gunsmith can often get it on, but, it is not 100%.
The people who run Ithaca, now, will bore the threads out of the receiver of an old gun, and install an insert, machined to take one of their new barrels. I don’t know if they will do a 16 gauge, however. I wouldn’t recommend it anyway, as the barrels they produce today are heavier, and cut for choke tubes and steel shot.
Best of luck.