How do I punch enemies instead of using a melee weapon?

Sometimes when fighting weaker enemies, I want to avoid using my melee weapon to preserve weapon durability for tougher fights. Unfortunately, the melee button always uses my melee weapon if I have one. I can't find any way to drop my melee weapon unless I find another weapon to swap it for.

Is there a way to punch enemies instead of using a melee weapon I've picked up?

Unfortunately you cannot actually do this without dropping your melee weapon entirely by either breaking it or by picking up a brick which is quite common. Another alternative is that you can then throw bricks to kill weaker enemies.