Depending on what the barrel was to begin with, going all the way down to 16-18" would be a pretty substantial loss. The loss would not be linear either, the shorter it gets, the bigger the loss, per inch. I'm thinking that he would be looking at something like a 300+fps loss, going all the way down to 16"...but just guessing there.
I can tell you that when you cut any single shot firearm down to 16-18", it really becomes too short, and will have an odd, clumsy look and feel. It will become VERY "butt-heavy"...way beyond just being muzzle-light.
Going down to 24" will produce a very short carbine, but it will still have some "proportion" to it...won't be so out of balence, visually. Can't really find the word I want here. I would at least urge him to cut it to 24", mock it up, before deciding to go shorter. Again, that will produce a more balenced, better handling carbine, and it will still produce reasonable velocity. It would be a more useable gun, rather than an oddity.
I have a 24" barreled half-stock carbine that was made from a Zouave...it's a light, handy little short snorter. Neat little carbine, but any shorter than that and they just don't look or feel right.
Rat