Almost all vintage SxS's have full tapered chokes and as Edgar has written it's fairly easy to carefully tap down the choke bulge against a mandrel made on the lathe to exactly match the choke taper. Then if desired the outside of the tube can be "struck" and spot reblued. I've done that a few times now on different maker guns and with excellent results. Note that I'm a hobbyist and only work on my own guns but IMO it's worth a search to find a good 'smith with in-house metal lathe and available time to do that before cutting the tubes.
Here's one made for bulge in the leade of a Fox choke, you can’t see its .013" taper in diameter over the length of the mandrel. Bolt and washer hold it against the muzzle while tapping. That's blue Dykem over the steel.
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