To qualify as a US martial pistol, the maker would have to have been, the arsenal at Harper's Ferry, in Springfield Mass or under government contract by Henry Aston or Ira Johnson of Middletown Conn. or William Glaze Columbia SC doing business as the Palmetto Armory. NP Ames Springfield Mass. and lastly Henry Derringer of Philadelphia.
The Ames and Derringer made pistols have a sightly shorter barrel and flattened capped pistol stock.
Theirs also a 1843 US army signal pistol with lock marked as such smooth bore.69 cal. and a later one muzzle located flair holding device in .75
The secondary pistols were those like the Waters made for speculating a contract or supplying state troops, semi official military personnel and Naval organizations like privateers or those wanting to arm themselves accordingly. Elgin and S North may have produced similar pistols with minor difference in lockplate and the cone/nipple and hammer just like the Waters.
I have a real nice one of these (see picture). They are 54 caliber, smooth bore, shooting a .530 diameter patched round ball. In addition to Henry Aston, they were also made by Ira N. Johnson, also of Middletown, CT.
24,000 of these pistols were made by Henry Aston between 1846 and 1850, and were marked H. ASTON on the lock. An additional 6,000 were made in 1851 and 1852, and were marked H.ASTON & CO.
Ira Johnson, a former partner of Henry Aston, made 10,000 of these pistols, which are dated 1853, 1854, and 1855.
If you use the correct materials, there is nothing in the world wrong with giving this old gun a good cleaning. First of all, don't polish the brass. The iron parts should be soaked in Kroil or any other good penetrating oil. Then scrub the iron parts with 000 or 0000 bronze wool. DO NOT use steel wool. The penetrating oil and the bronze wool will remove the rust (of which your gun has plenty) but will not damage the iron parts. You can wipe the wood down with any good furniture treatment. Do not sand or use steel wool on the wood.
If you're not comfortable doing the work yourself, you can take it to John Zimmerman in Harpers Ferry, or to R.A. "Bobby" Hoyt In Fairfield, PA. Either of these guys can do a good job on it, and can probably make a replacement for the missing brass piece on the side opposite the lockplate. You might ask them to give the bore a good cleaning, also. It bore might be good enough for you to shoot it. I shoot mine, and it's a ton of fun.