I agree that a shotgun would be useless, and that a typical melee weapon would not fit well in a game like this.
However, there are a few other things that my drunken mind can spew.
1. Aggressor Shield. Did any of you play the Independence War games? This was a "grinding" forcefield that you could trigger on your spaceship, that made your ship do a huge amount of ramming damage, while minimizing the damage the collision did your own ship (it did not protect against weapons.) (I-War 2 had an automatic variant that triggered right before a collision.) Replacing one of the held weapons with something like this (and perhaps having it triggered by overdrive) seems like a good fit for this game.
2. Sticky bombs. Simply put, a launched or thrown grenade with a small amount of splash damage that sticks to wherever it lands, including enemy players. Making them detonatable would expand their usability. Making a "boost" variant of this could also be cool.
3. On the same ilk, a disintigrator knife. Make it the sole weapon (or perhaps alongside CG/Plasma only) on an Outrider or perhaps an even lighter class. Point-blank, stab, run, 3 seconds later, insta-kill. It would be difficult to use and the user would be disadvantaged at range. This might be a good weapon for a HOF though.
4. Disabling weapons. This could be applied to the stickybomb or knife idea. Hit them with this, and an enemy's suit shuts down for a few seconds (this could vary based on the class.)
5. Addendum: Flamethrower. It's not as cool or original as the other stuff here, but it's FIRE. Nuff said.