The airplane that Steve Austin flew to the island was a C-130, but the interior scenes of them preparing to jump from the airplane door are from a C-47.
A nuclear warhead is very heavy, so nobody could just two-handedly scoop it up from among the downed plane's wreckage and scamper off with it on his shoulder, especially when it is still housed in a sturdy metal (and probably lead-lined) protective case.
Both Steve and Oscar are guilty of the oft-made error of pronouncing "Nuclear" as "nucular".
When Tomas picks up the photo and speaks to his men, his lips do not move.