That is what I was talking about - I call them stalking safeties - very different from a stalking safety on a hammerless gun.
Actually, I would think the purpose of a stalking safety would be the ability to take the gun off safe with minimum noise. Certainly true with the small hammer safety mounted either fore or aft of the hammer, but not so with a hammerless. Simply because you move the little lever over and then still have to "click" the safety forward - certainly no quieter than a standard safety.

I personally don't know what purpose the little safety blocking lever serves on a hammerless, but they are cool looking. Maybe if you have a tendancy to accidently slide your gun off-safe.

Do the safeties on hammerguns block the hammer at full cock only? This makes sense to me, because the half-cock position is in itself a safety of sorts. If your gun had a worn sear, it would be nice to use the safeties at half-cock too though.