I always "run the slide" if I am interpreting what you are saying. Versus using the slide stop/slide release.
I don't think it matters that much if you push the gun forward or pull the slide back as long as you are consistent and train that way.
Either way, it won't hurt the gun.
I try to do the same thing every time.
If I have a malfunction, I Tap/Rack.
If I load the gun, I Tap/Rack.
If I swap magazines, I Tap/Rack.
I only use the slide stop/release to lock the slide open for administrative reasons/malfuction clearance (phase 3).
That way it works the same offhand/primary hand and no matter which gun I am using. (I forget where the slide release is on a Sig sometimes.
)
I think that is what you are asking about.
If not, can you clarify?