Gas mask and a few teargas charges ought to work OK too. Problem is that the Heart likes to close up the walls on its level…so it’s possible to get cut off from the upstair and/or the Heart. J-Hammer FTW.
As for whether the nuke silo ought to kill a heart, assuming we had the codebase to support it: two levels underground? depends on the size of the nuke. A full ICBM ought to expose the Heart (remove the intervening soil, etc) but the Heart could luck out and survive.
(edited to clarify that a Silo can’t kill things underground)