I always consider stealth, or discretion if you prefer, when moving something like a safe. I think it is worth the time and effort to minimize the number of people, and the types of people, that know you have a new safe, and therefore something to protect.
If you can make it look like a new fridge while going from the truck/trailer to your house, I think it would be a plus. This can be as easy as obscuring any safe-specific markings on the box, or even repackaging the safe in an old fridge box.