I use a regular strop all the time when traveling. Lay it flat next to the wall of a rigid or semi-rigid bag in a plastic sleeve and it should travel just fine. Takeshi at AFrames Tokyo sells strop cases if you want one. This way I don't have to buy or learn to strop on something different than I am used to.

Take a piece of paracord or thin climbing-style cord and you can anchor the strop to a doorknob, shower rod, towel rack, etc. I usually carry a piece of cord several feet long and it doubles as an expedient clothesline.

Cheers, Steve