This is a rather crazy question, but how would a pickaxe fair as a weapon?
If it’s a weapon of opportunity, then fairly well. For example, if you have a character in a struggle against someone else, they’ve lost their weapon, and the only thing they can reach is a mining or climbing pick, that is going to mess someone up.
There’s a bit of a bonus here, the pick’s beak is an excellent armor penetration tool. So, in that very narrow tailored situation, it’s a good option for a single surprise attack. A lot of real weapons, including pole-arms and warhammers used similar pick designs for this purpose.
Depending on your setting, your character might carry a pair of ice axes. These are, basically, single beaked climbing pickaxes, designed for digging into and scaling ice walls. Again, not a weapon, but if it’s all your character can reach, they can still probably put one into the skull of an unsuspecting enemy.
A pickaxe isn’t a great weapon for a straight up fight. Limited strike options are the big issue here. You need to swing it in a fixed, linear, path, and against an armed opponent who can defend themselves, that just wouldn’t work.
The main difference between a war hammer, and a normal pickaxe is the weight and reach. These were (usually) longer weapons, with a single beak, a blunt face, and a head that could be used in linear thrusts (sometimes with an additional spike on the end). This meant there were far more options to attack with one.
For whatever it’s worth, an ice axe is much closer to a warhammer in overall design. It still has an adz opposite the beak, but the overall design is much lighter, and probably more versatile than an actual warhammer. Ice axes have a spiked haft allowing you to (potentially) use it as a thrusting tool. To be fair, I am speculating a bit, and it would depend on the materials and design of the specific ice axe.
If the idea is, “my character has a pickaxe as their favored weapon,” then no. That wouldn’t work out. However, if the idea is, “my character is desperate, and the only thing they can get their hands on is a pickaxe,” then, yeah, there is some utility there. Especially against a foe who doesn’t see it coming.