There's no way the BHP made it into every conflict since 1935 (at least if we're limiting this to officially issued weapons, be they standard, substitute-standard or irregular issue), but I will easily believe that it has done so more than any other sidearm. The 1911 has been around since, well, 1911, but we're really the only major military that uses it. The British were a massive military presence, and most of the commonwealth nations used or still use the BHP, and there were a LOT of wars created by the death of that empire. The BHP probably served in each and every one of them, right up through and including Gulf War I and II and the Afghanistan conflict.
Mike