Use a box a couple inches or so larger than the contents in each direction. The best packaging material is something firm but a little giving-- the expanded foam pieces (like what supports a TV, etc., inside a box) work best, forget about most bubble wrap. IME boxes take pokes from other stuff in transit, and having the items isolated from the sides of the box is a good practice. I always keep all packing materials that come into the shop (as well as personal purchases) so we can use it for stuff going out.
Lacking foam you could use heavy cardboard, perhaps even cutting strips and laminating them with glue and/or tape. Build a framework to support the cab and isolate it from the box. If you don't feel comfortable and/or cannot isolate and securely pack the lightweight head with the cab, ship it separately.
Many moons ago, before I got into the business, I had a personally owned URB shipped to California; the buyer made arrangements for the packaging and shipping. I watched the Package Store guy wrap the bass in heavy plastic (already inside a a padded bass case), put some cardboard supports on the bottom and back of the wooden crate he'd built, and then he sprayed expanding foam into the box all around the bass. Just another concept, you can buy a can of expanding foam and try something similar.
OTOH you could take them to a UPS Store and let them pack it. It's probably some pretty heavy bucks, but when the same company is responsible for packing and shipping it, there's no finger-pointing if there is damage in shipping. That said, we (knock on wood) have an extremely low incidence of problems with stuff we ship by UPS.