If you *don't* give her a melee weapon, she will use her default melee weapon, which is a Chinese Officer's Sword.
If you're playing the PC version, you can get "Clover's Cleaver", a unique version of the Chinese Officer's Sword, and give it to her. Just type "player.additem C80B8 1 100" into the console (without the quotation marks, of course).
Clover's Cleaver can be repaired with any other Chinese Officer's Swords. It was originally intended for her to use this unique weapon, but due to Bethesda's usual level of competence in programming, it was left out.
She will favor any melee weapon you give her, especially a Shishkebab, over her ranged weapons, but you can tell her to switch to ranged weapons. To me, she seems most effective with a Shishkebab.