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Put the safe in the trunk area and park with the trunk pointing away from the building. You can go get your lightweight jacket (which happens to conveniently be in the trunk) for going into the air conditioning and then put it up in the trunk when you come out while you get your gun. Say you're going to get your jacket out of the trunk while the passenger is otherwise occupied and you're already halfway there in a way which says the person need not follow as you'll be back before it is worth their trouble. Or you can always "forget" your jacket half-way through the parking lot, but then you risk an attendant hanging on your every word walking back with you or offers to use theirs or something harder to navigate.

You can also make an excuse about not wanting to carry around your heavy purse, pull the pocketbook with the chapstick out and just carry that while locking the purse in the trunk.