Hello. The Browning HP Mk III is my favorite of all pistols though I prefer it in 9mm. I've been a HP owner and shooter since '71 and own some of the "pure" Belgian guns and still prefer the newer Mk IIIs. I own one MkIII in .40S&W. This handgun groups well with loads it likes and is reliable although my particular gun is a little fussy with very blunt, short rounds. It works fine with Winchester Silvertips and most other high-performance rounds, but really short, blunt rounds like some of the 135 gr will jam one tries to cycle one into the bbl from the magazine, but this does not occur when the weapon's fired. I can live with it as I prefer a handload using the 180 gr CTC bullet and usually shoot 165 gr jacketed HPs for the warmer loads. I removed the magazine safety from my forty, which some wisely counsel against, and added Uncle Mike's rubber stocks that are based on Spegel's original design. I had Novak sights added and black parkerized the entire pistol. In short, I think that the MkIII in .40 would be a fine pistol if you respect the "lack of error" tolerated by practically any single-action design. Best and good shooting.
