What handgunner356 said.
Last time I asked about 4566 barrels I was told that S&W still has some 4566 barrels in inventory.
The TSW barrel has a thicker hood than the barrels used in the standard 4566. They would have to modify a TSW barrel by hand in order to make one fit in any particular 4566 slide. This is one of the problems S&W experienced when they were having to make some of their new production TSW barrels fit in some older 4006 slides of CHP guns. I spoke to one of the techs who had done this. It apparently wasn't a quick process.
There's even been some changes in the barrels used in the TSW series. I had a couple of 4566TSW barrels out of guns made within approx a year of each other and noticed some obvious machining differences. In that instance I was told the design changes were for simplification of manufacturing and that the barrels could be used in any 4566TSW, as long as inspection and bench checks confirmed normal fit and function.
Every once in a while, though, it's not unusual to find that one barrel (or other part) may not work in one specific gun, but will work fine in other guns. Just depends on the combination of parts and their aggregate tolerance stack.
I agree it's best to let S&W check your specific gun and install the appropriate barrel in it, so they can check for proper fit & function.