Depending on the length of stay, have more diapers shipped to your hotel (direct from store) for less luggage to carry.
Airport security is a nuisance but you need not worry about it nor take extra precautions before passing through it. As mentioned, if you get searched just tell them it's a diaper, they've seen it before, it's not a big deal wet or dry. You may get extra pat down and scanned for explosives, but they're as uncomfortable as you are and just want to get you on your way.
Hotel staff expect private things to be in your private room, and will pretend they don't see it... The only one inconvenienced by disposing of diapers outside your room (instead of using the trash receptacles inside it) is you. While there may be water cooler talk among staff, they're in the business of hospitality, not making you uncomfortable - they want you to come back unless you're a bad guest, and wearing diapers and disposing of them appropriately is not being a bad guest. There are many other interesting things guests being and leave out in their rooms than used diapers in the trash bin, lol. If your room isn't cleaned daily or your diapers are stinky, it isn't a bad idea to single bag them in used diaper sized bags - there are bags sold for this purpose or you can repurpose other disposable bags.
Traveling diapered is no different than being home diapered. Have your diaper bag close at hand when out and about, and wear the protection your used to. Leaks suck, trying out different products for the first time is always an opportunity for learning their limits the hard way, you don't need that stress or extra cleanup while away from home and trying to enjoy your vacation. If traveling over seas and you want to order diapers, do some research to make sure the locally available/ordered product is equivalent to what your used to at home. For example, while pullups may work for some, they'd be miserable for those of us used to not changing as often. Different diapers hold different amounts, etc.
I've found the worst thing that can happen is running out of diapers, so over estimate your needs because not having enough is not pleasant...
Just my two cents, use what you find useful!
Have a super enjoyable trip, and do so diapered if you want!