While playing some local Combat Training, I stumbled upon a bug whilst sniping; whenever you pull your radio to signal an airstrike-based killstreak, put it aside and immediately bring it back up. You'll then notice you won't have up the minimap - rather nothing at all. Instead your character will have a radio glued to his hand the whole time as you move.
After screwing around with another controller, I've confirmed my findings. One thing to consider is that you'll need Scout Pro to get it done fast enough. It's nothing practical, but would be nice to screw around with in parties.