Guild Wars 2

I’m not at home but the idea came to me today and had to know if it counted or was possible.

If my secondary weapons are the same as my primary ones and I switch to them, would that COUNT towards a different Cooldown? OR would I have to wait in general for my weapon skills in general.

(Find a better way to word it.)
I got a pistol as my offhand mesmer
switch weapons and still have another pistol offhand as mesmer. Would the same skills be on cd?

Nope, they share the same cd.