Those pistols were supplied by the Board of Ordnance to allied Indians in Canada. By all accounts it wasn't a success and very few found their way to the intended users. In any case, they are quite rare. I forget the exact numbers but it was no more than a few of thousand, if that, compared to the tens of thousands that were imported to the US before the War of 1812. You are correct, if it was one of those it would have an ordnance storekeeper's mark and, even in that condition, would be considerably more valued. When found they are often in pretty good condition suggesting they were mostly held in storage and sold off after the war as surplus. They were never of high enough quality to be issued to regular or irregular British troops or Canadian militia.
Note: when you say "trade pistol" are you implying the "Indian trade"? If so, this is completely erroneous. They were "trade pistols" in the sense that they were made specifically for the American trade. Very very few found their way into the British domestic market (I know of only one example marked to a Yeomanry unit)...they were a specialized inexpensive pistol made to sell in America. Pistols were generally carried in saddle holsters on horseback, which explains why native Americans had little use for them. If a person was going to carry a pistol it was invariably a "pocket pistol". This must have been very common because those survive in greater numbers than just about any other flintlock.