Nothing Federal, but the State has issues with individuals "importing" firearms, including air guns and Muzzle-loaders.
If sending to an FFL for a transfer, no problem on shippers' end.
Not true. Air guns and muzzle loaders are same as mainland US. What might be different is mandatory registration. As everywhere else, Firearms must ship to an FFL.
I thought the op’s question was related to which common carrier to which I’d say “flip a coin”. Each has had occasional problems. Pack well, insure and make sure you get tracking to up your odds.