idreamofcrusing- get the notarized letter. Most likely you won't need it but you don't want to be standing at the cruise check in counter and find out he would be denied boarding. At 18, they might not ask, but then again they should. Better to have yourself covered.
As for the cave tubing, they won't ask nor care how old he is as long as he pays the money.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013