I prefer the hanging strop, and like the Dovo 185-35001 because the leather's nice and it just barely fits in my leather toiletry case. It can also fit in the mesh divider thing in my luggage.

I bring a piece of Rip-Tie cable wrap, which is insanely strong and reusable thousands of times, to get the little strop to hold onto towel racks, doorknobs, whatever's available.