Personally, this is a whole buncha mountain out of mole hill to me. If you aren't comfortable taking the order then turn it down. But voice of reason here... I have done many yacht weddings. I think you think that whoever driving the yacht will be hauling butt doing doughnuts around the bay/lake/ocean trying to win the America's Cup. Well let me tell you, they putt-putt around and go super slow, they also do whatever they can to prevent the boat from pitching. The last thing they want are guests falling over, drinks spilling all over the place, and guests puking from sea sickness especially in a situation, like a wedding, where people are eating and drinking a lot. And, I don't know if you live in an area that has real yachts, but if you do, and this wedding is on a real yacht, those things are more solid and soft floating then anything you can imagine. I am going to take a stab at guessing this is a huge boat based in the cake size requested and not some outboard tiny schooner.
When I do a yacht wedding (well, any wedding but I'm particularly on my game for these), I make sure my interior support is perfect. If you are worried just use SPS. I always refrigerate my cakes prior to transport and I would suggest you do the same. Yachts are air conditioned and have kitchens larger then your home kitchen- it must be, after all, in order for it to accommodate catering for hat, 150 people? It may even have a walk in or several walk ins, depending on the size of the boat so I seriously would not worry about the cake melting. They aren't goin to mount the thing on the deck!
I also regularly let people pick up tiered cakes. As long as you speak to the driver on the phone, DO NOT RELY ON EMAIL, to explain what kind of car they need to bring, that it needs to be clean, have a flat surface, and not drive like madmen, it will be fine. I always provide a strip of rug grip so the cake won't slide around as part of my service. Then have them sign a waiver.
As for the cream cheese icing hysteria, google it. It's shelf stable. I don't know why people are so paranoid about it, it's even OK in most cottage law states because its shelf table. Some recipes are more crusting and firmer then others, but use what you are comfortable with to get it on the cake. There are several recipes right here in the recipe index that are great like Indidebi's and I think Sugar Shack has one.
Anyway, I say take the order!