Using the Crescent activates a 20 second cooldown on the skull.
Using the Skull does not activate any cooldown on any other trinket.

So just be sure to use the skull first. For realies.

/stopcasting
/use The Skull of Gul'dan
/use Icon of the Silver Crescent

note: this may be a bug, and might be fixed in the future

EDIT: Patch 2.4: "Skull of Gul’dan: This item now shares its cooldown with other similar trinkets."