1. Find a good spot for stropping and screw one of these into the wall.*
Attachment 104357
2. Find a good spot for storing the strop. If you don't have a convenient, seldom-used drawer, then screw another eye hook into the wall in an out-of-the-way location.
3. Snap a little carabiner onto your strop's hanging end for easy 'n quick transfer.
* If necessary, learn (or promise to learn) how to fill and camouflage a tiny hole in the wall. Then convince your wife/girlfriend/mother that a tiny hole in the wall is no big deal, in the grand scheme of things.
Good luck!