Are you allowed to use a Scuba hookah system w/o a scuba certification?

There is actually a Hookah diver certification. So the short answer is technically this doesn't get you around it. --- diving a hookah is still breathing compressed air at depth and still has the normal effects of depth on the body. So there is still the issues of equalization and still a danger of over expansion injuries. ... That being said, there are a few ways to "bend" this. Where is the wedding being held? If it is an area that an instructor is able to "bend" and define as confined water, and if all the folks are reasonably healthy, and take a bit of "class time" before hand, you may be able to get away with a discovery dive or resort course type of deal. However, for the folks that have little experience underwater, it may be beneficial to have like a pool session the day before, just so they can see if they can do it. Last thing you want is someone who thinks it is nothing to be done there, freak out and get injured at your wedding.

I'd speak with the shop / or place you are having it and see what they can work out for you. It really depends on where you're going, how many people you want down, and are you willing to have a few "safety divers" around. (as any time there are uncertified divers in the water there are ratios of how many instructors/divemasters must be close at hand)

Good luck!

Scuba Diving