I think this would actually be a good skill for any weapon. Consider replacing the sniper restriction with it being use able for any weapon, and making the damage a multiplier instead of a fixed damage.

So.... That's a no on my suggestion to make the skill available for use with any weapon?

Alright

Can you fire multiple times per round with this skill when using... Let's say... A pistol? Thus doubling damage for 6 shots in one round?

In that case, change:
"Can't stack with itself. Only usable once per round."

To:
"Affects only one shot per round"

The can't stack with itself part is useless, since you can't use multiple skills at once.

Very well

Change
"To use must be touching the enemy with the gun."
to
Melee range

With that aside, the weapon seems pretty low power for anything but rifles. Either increase the multiplier, lower the stamina use, or remove the restriction of affecting only one shot per round.
I would favour the latter of those three as the best option.