I have a moment, so Ill throw in my two cents.
And I am completely unfamiliar with the modern shotgun about which this thread was started.
However, Its not uncommon for an aftermarket choke tube to have the choke section outside of the carrier barrel. I have seen, shotguns that had after market thin walled choke tubes installed in them, that didnt have enough wall thickness in the threaded area to keep the barrels from splitting.
So, I would encourage you to have the Smith vett all of that with micrometers.
Just a word of caution before cutting off any choke tubes.