Welcome back.

I've received some strops flat in a long box and some in a loose roll and either way they have been fine. Good quality supple leather is pretty flexible so it can handle it with no issues.
As mentioned here in US we have various flat rate boxes which work quite well. I sold some of my 3" strops in the last year and that's how I shipped them. The medium comes in two sizes 11 1/4" x 8 3/4" x 6" or 14" x 12" x 3 1/2".
I thought that the second one doesn't fit very well and could compress the width of the strop so I've used the former where there's plenty of room.

Cling wrap is a good solution. I also use tissue paper first.