I am still with one thing stuck. The enemy must not drop weapons the player can use. So they either have to shoot with something the player cannot use or I should explain why the weapons disappear. Any Ideas?
I believe no one has mentioned the option of their weapons being part of their body yet?
The intelligent race solution: Their race breeds for optimized usage of the body. So whereas scientists are bred for intelligence they also have multiple arms/fingers etc. to operate faster. The fighting force is created to be ferocious but loyal and submissive to their overseers. To optimize their battle capabilities and prevent their advanced weapons from being used against them they breed their fighter with their weapons as part of their body. Either instead of hands/limbs or above the hands on the lower arm .
As for the less intelligent race solution, just go with the last part really. There's no reason why alienish creatures would have sharp fangs/claws but not guns. If you don't want to go into much story overall just having an enemy sprite/model that has an arm as a gun is already enough imo.
Of course humans cannot be extremely advanced in bio mechanics or they would still be able to utilize the weapons in some way. Also it seems rather unlikely that they would shoot with bullets as ammunition, a gooey acid like substance would be better suited imo but there's room there.