Firstly a BHP is a bad example to try this with - either model of safety is tiny, easy to miss, and not very positive in letting you know it's actually deactivated. You can remedy it with a C&S extended safety (or one of the other extended safeties). Secondly, it's also not comfortable to shoot that way, as it's not very sleek. The safety isn't blended into the frame at all and can cause discomfort when shooting.
Or you can start trying to learn to do it on a 1911...like everyone else in the civilized world
The safety is easier to hit, far more tactile, and so long as the parts aren't stamped out of a piece of sheet steel can be made very slick, so that it won't have any negative impact on your thumb or the joint.
BHPs are very much the odd man out when shooting that way. Really, 1911's are king of that hill.
The same grip is transferable to nearly everything; Glocks, M&Ps, etc. It doesn't translate so well to Sig P-series/classic guns because of where the slide release is..but that's a minor grip adjustment.
It also doesn't translate well to revolvers...unless you enjoy blowing chunks off your thumbs