They mentioned radioing number 3 to set off the nuke if the mission goes pear shaped, so I'd assume they have a hand held radio of some sort.
Course the nuke needing a trigger command is a flaw in their plan, if 1 and 2 get killed before they can call then the nuke is left out of play unless 3 decides to use it on their own. A better method would be periodic check ins to prevent the nuking, but then that would jeopardise the stealth aspects of the mission.
In any case, I imagine the JSP will get killed at some point, which will then leave the nuke as a floating problem because there's no longer a way to tell number 3 that Cheryl is about to be neutralised if he winds up in a situation where he's going to die anyway.