In case you'd like a third alternative…

I always have a couple of newspaper strops in use. Both are VERY lightly impregnated with mineral oil.

One also is marked with just a few X's from a Chromium Oxide crayon. That one is labeled "Hone." I use that strop to clean off any hone debris off of a freshly honed razor so that I do not transfer any debris onto a linen or leather strop.

The other strop is labeled "Shave." That one is only used to clean up an edge after shaving.

Whether concerned about convexing or not, both newspapers strops are held taut. A great advantage of the newspaper strops is that they are entirely disposable.