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?