So I'm going to be a massive wet blanket here and say, that after years and years of shipping things to customers, I ALWAYS try to talk customers out of shipping things to hotels. It is just such a bad idea for a million different reasons. Things get delayed, things get lost, bad things happen.
Just two very easy to understand scenarios (they can get vastly more complicated):
You're shipping something to a hotel and it gets delayed and shows up after you've left. Then what happens? Somehow you've got to figure out how to get someone at the hotel to A) know what and where it is and prove who you are and where it should go and then B) get it shipped back to you. This all is non-trivial.
Another common scenario is the item arrives on time, but the hotel doesn't know what to do with it. Keep in mind, you may feel like you had a very clear phone conversation with a hotel rep, but that person probably talks to hundreds of people per day, and is one of a dozen or more staff members working at that point in time. Your conversation was not memorable, and that person is unlikely to be the one who actually receives the package when it is delivered anyway. A real problem with businesses people don't realize is communication, how do you reliably communicate a non-standard request to everyone else on your shift and on the next shift with information which may not be important or relevant for a week or more? It is actually really really hard, not just for hotels.
See what I'm getting at? So, again, while it doesn't always turn into a mess, based on my data it has about the same success rate as shipping something valuable to Russia (the other lowest probability delivery, yes it is worse than Azerbaijan by a substantial margin) ergo I would very much encourage you not to do it.
Flip side of the coin is that, as Centercut noted, it is really easy to fly with firearms. A buddy of mine would actually toss a fare gun in his suitcase and check it as a "firearm" because firearms all ship chain-of-custody so at any given point in time there is a specific person whose ass is on the line if your weapon disappears. You on't be able to pick your suitcase up at the carousel, but that is a small price to pay for "it absolutely positively will show up." So yeah, of the three common options (ship it, drive, or fly w/ it checked) I'd probably go with flying with a checked firearm.
I hope that is helpful. It is just my 2c on the subject. I'm sure someone here will tell me I'm crazy and they've shipped stuff to hotels no problem, but having made that mistake dozens of times now I guess I just can't recommend it. *shrug*