The BHP made by Inglis for the Chinese and having the original shoulder stock/holster has been determined by the BATF to be curio or relic and removed from the purview of Title II of GCA68. In other words, it is a pistol; the stock is irrelevant. Note that this, AFAIK, this is the only BHP involved in the ruling. This is the same ruling that was made in the case of some Luger and Mauser pistols with original stocks or stock holsters. These determinations are very precise, affecting only the specific combinations described.
If the pistol you describe was openly displayed I would assume it was one of the ones described, or was registered as a SBR.