Only one race in the players handbook has an innate weapon aside from just using their fists: Dragonborn with their breath weapon. This leaves them always armed even without handheld weapons.
The damage starts at 2d6 and goes up to 5d6 – so not an overwhelming amount. However, the cool thematics see breathing fire or lightning is off the charts!
Pro-tip: choose a class that allows you to disguise yourself and you could appear to be an elf…breathing fire.
DM Thought: as the damage of the breath weapon is not very large after the first few levels, consider letting a player use the weapon 1x turn instead of 1x rest. Is that overpowered… only maybe: remember it is a short range, they cant change the damage type, and it uses their action just like an attack or spell.