A paddle strop or a travel strop along with either a leather case or a toothbrush case to hold the razor would be a good place to start.

I have used a 2" strop and wrapped it loosely inside a spare belt in my bag. Didn't have a problem with that.

You could also do a set of razors so you have one for each shave and strop at home.
Or you could do a Shavette (Dovo has options to use their long blades, long personna blades or a DE blade snapped in half)
Or a Feather AC
Or DE
Or wax your face before traveling
Or hire a manservant.
Personally, I'm a fan of the manservant idea but in too cheap. So I usually travel with my Shavette and a DE and if I'm doing carry on only I either send blades to the hotel or pick up some cheap Wilkinson Sword blades at the local wallymart.