The game is very well made, uses the theme well.
I do feel that if you are going to have a firing mechanic with a cooldown but no other limitations, you should be able to keep firing by holding the button down. Especially after getting the firing speed upgrade, the rapid clicking gets tiring on the hands.
I also think losing the weapon after one hit is pretty harsh, the randomization means that sometimes enemies will be blocking your only path, so with no way to shoot them you have to take another hit and possibly die.
Also nice use of a limited color palette.