restoring vintage linen strop

I got a vintage horsehide shell, and linen combo strop off the bay.
The shell strop was in decent shape, but I did the lather and roll with glass bottle as suggested elsewhere on the forum and will see how it turns out tonight when I get home.
The linen part has worn away whatever waxy dressing was on there before and is wavy. What is the best way to try to flatten the linen portion, and what would be best to redress the linen portion?

thanks.

I have had good luck with a number of lumpy/wavy vintage linens by washing them in cold water with Woolite. Then laying them flat on a table and letting them air dry. I've also washed one in the machine with clothes but I like the hand washing better. They dried flat and little or no waves. As far as re-dressing, I don't but I've heard the white strop dressing is either mildly abrasive or not at all. I think Dovo makes it ?

Thanks Jimmy. I will give the woolite hand washing a try.