Reading between the lines - --
justashooter, all the underhammer firearms I've ever seen were percussion muzzleloaders. If you're considering one of these, you should be okay. Barrel length, overall length, and bore size seems to have no importance in this sort of arm.
I'd worry about you building a cartridge firearm, though, especially using a bore size over .50", which ten ga. certainly is.
I've seen some single and double handguns using 12 ga brass, but they had to have rifled barrels.
Please use caution to ensure you don't get crosswise with the law, just trying to make an unusual piece as a hobby project.
unspellable - - I've seen illustrations of such pistols with side hammers (spurs to the top OR angled to the rear,) as well as "hammerless" designs. One of the latter, made by Lancaster in England, was even a four-barrel.
Shootcraps - - I'd imagine a faithful replica of a breech-loading, rifled barrel Howdah pistol might well be illegal. If one came up with an authentic, 19th century, Howdah, though - - I imagine it would fall under the exemption list.
azrael - - I think you're right, in regard to purpose-built Howdah pistols being rifled. At the same time, I can certainly envision local gun mechanics in India and elsewhere, doing conversions of sporting shotguns to Howdah configuration.
Interesting topic, this.
Johnny
Best,
Johnny