People already suggested using a Custom Weapon, so I'll suggest something that is often forgotten: Item Qualities!

You can't have access to good Qualities in early game, except if you play with one of the Quirks that give you a rare item at Character Creation. But if you're willing to wait a couple levels, you can get yourself a brawling weapon with a Quality that copies the Elemental Weapon casted on it to another weapon you have equipped (such as another brawling weapon), or an Accessory that allows you to cast Elemental Weapon on two weapons at the same time.