Verified answer

You do not have to use any Trap card unless you choose to. If that was the case, cards like Solemn Warning and Torrential Tribute would be going off on your own summons; clearly that has never happened.

This also applies to cards like Dimensional Prison and Mirror Force.

This also applies to cards like Gorz and Tragoedia.

This also applies to more versatile cards such as Compulsory Evacuation Device and Book of Moon.

You never have to activate any Trap card unless you want to and no card in the game of Yu-Gi-Oh forces you to do so (except Bait Doll, but that doesn't even apply to this situation).

You may use a trap card at any time unless stated otherwise by the card itself and as long as the activation of said trap card is used at the proper time.

you CAN save it for later, unless they have a card that forces you to activate trap hole. if they normal summon a celtic guardian and you know they have a summoned skull, you can leave trap hole set and save it for summoned skull. but trap hole only works on normal and flip summons, so if they special, xyz, synchro, ritual, or fusion summon it won't work.