How do I taunt specifically with my weapon?
As far as I'm aware, the only way to avoid this is to begin your taunt far enough away from the conga that you are actually allowed to do your weapon taunt, then pray your enemy congas right into it. I do wish there were a more positive answer for this question, but if you consult the wiki you'll see this on the item text.
This is a group taunt. Other players can join you by activating their weapon taunt.
Given that your weapon taunt is where your tauntkill is, using it while near a conga is not going to happen.