I was looking at an Alex Henry 577 double I just got.
It has what most would consider "stalking safeties" but instead of holding the hammers at half or full cock, they keep the hammers at their rebounded position.
I had not considered the need to hold the hammers in their static rebounded position before, but when you think of it, there is a need to prevent an accidental discharge in the event the rifle falls or is dropped.
The rebounded hammer, sitting off of the striker, could fire the rifle if struck in that way whereas a non-rebounding hammer is already fully down when closed and the hammers let off half cock.

So, to my mind, these safeties are not at all "stalking safeties" but simply a safety to prevent accidental discharge.
Truly, by name, a Stalking Safety should keep the rifle safely at FULL cock so not to make any noise when bringing the rifle ready while stalking game.
Admittedly, the hammer safeties which I have been calling Stalking Safeties for years tend to hold the hammers at half cock which lend little to being silently actuated in a quiet hunting situation.
Better noise control than a full motion of the hammer, but not really that silent.