The photo is my basic travel kit:
H&S N075 for razor,
Cream for soap (if not the ADP then DR Harris Arlington, both are TSA compliant. If it's a long trip, say a week or more, I may carry both)
A synthetic brush (either the pictured APShave handle with G5C knot or a Rudy Vey handle with at Muhle STF knot)
A tube of balm (usually, as here, DR Harris shave milk),
A small size sampler of aftershave splash (here, again DRHarris, but sometimes its Phytomer Rasage Perfect or one of the cooling Summer Break splashes; sometimes more than one splash since the little sprays are so small).
That all fits in the little first-class goody pouch from American Airlines, with a bit of space for something else as well.
If flying and going the carry-on route, I will remove the blade from the razor and have two packages of blades in two places in my Dopp kit, as well as a backup Gillette Fusion razor. I find that quite often TSA will not stop me and if they do, they usually only confiscate one package. But sometimes both. It's important to make sure the razor doesn't have a blade in it and to pack it separately from the blades. More often than not, I get through fine. If I'm going to a place with a Walgreens nearby I can usually buy a blade package and, if worse comes to worse, use the Fusion. But that's rarely been necessary.
Finally, I will usually carry a small travel size of scent, perhaps two; the one in the photo is in a small atomizer I got from Amazon and in which is Louis Vuitton Afternoon Sun (there's a label I put on that's not showing in the photo).
This combination works really well for me. The H&S is my most go-to razor (mild and non-irritating) and gives me a good and quick shave, so I do like to have it when traveling. If I'm in the mood I sometimes will thrown a puck of soap into my Dopp kit but I find both ADP and DRH creams work quite well.