Fitment is one issue, rather easily handled. The other issue is tougher.
The way the firing pin safety works is that levers from within the receiver should push the plunger in the slide up, and then that will allow the firing pin access to the primer. Without that lever, (I'm betting by mil-spec you're referring to a series 70 receiver) the plunger won't be pushed out of the way and the firing pin will take the hit from the hammer and mash into the plunger, WITHOUT striking the primer, hence forth, no bangy bangy.
If you decide to fit this slide to this frame, you'll either A: have to pull the plunger from the slide or B: have to mill the receiver to take the series 80 frame parts.
I wouldn't tell someone what to do with their gun, but if it were my gun I would pull the plunger, the firing pin, and the firing pin spring. Then I would use a series 70 pin and spring, and re-install without the plunger.
This will allow the firing pin to work and the gun to fire, but will also do the same thing that the series 80 design is supposed to do. It'll keep the firing pin from hitting the primer if you drop the gun because the series 70 firing pin spring is stiffer and more resistant than the series 80.