Removing Weapons

Does anyone have a way of permanently removing weapons from a character in online mode?

That's a pretty douche thing to do.
Unless you're talking about your own character.
In that case, no. Your guns stay with you upon purchase, even if you run out of ammo for it.

Yeah I wouldn't do that to a person. I'm talking about my own character because I hate switching through multiple weapons just trying to get a specific one.

You can set what guns are your default in online by playing story mode, as any of the 3 characters, set their gun wheel to what you'd like, and quick save.
From then on your online character will keep the same wheel.