Owned and shot often a suppressed 9mm SMG, LEGAL of course, for years, then sold it legally about 6-7 yrs ago for a decent price. AFAIK there is nothing in TN stopping one from shooting his legally-owned suppressed weapon..the operative word being LEGALLY OWNED.
IMHO do NOT mess around with ersatz, "ho-made" silencers or suppressors..they are a nono!
Bite the bullet and pay the tax, so you can shoot it legally. The movies make it seem that a 'can' the size of a orange juice concentrate can is adequate..do not be fooled. A decent suppressor for a 9mm or .38 size round will be about 2" in diameter and a foot long or so. They are nice..mine would suppress the 9mm so much that it sounded like a pellet rifle and you could hear the rounds impact ..on semi-auto. It would be OK inside a house, but not particularly convenient, plus they tend to block the guns' sights when screwed on...if that bothers you. Made little difference in a SMG to me.