If the barrel and your pistol were made during the same 'tooling period', no fitting should be required (in my limited experience). Variations exist in barrel hood width as well as the front 'toriod' (the bulge at the muzzle end that allows for a snug fit to the pressed-in bushing when the gun is in battery). TSW versions seem to have a different shape up front; I do not know whether this precludes interchangeability.
I would gently assemble the new barrel to the slide and check for free movement into and out of battery while making certain that the in-battery fit has no play. If this works, then try gently placing the slide/barrel/recoil spring assembly to the frame, checking again for smooth cycling and snug lockup at both ends of the barrel. Hope this helps...
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