Search:

Well its got a cut that would be nice to glue down and that might be course for some sanding.

I wouldn't put any abrasive paste on it at all, once you do it's there to stay and it has a tendency to spread...
The texture/surface on strops can be very different, do as little as possible and...

Now with pictures! :)

It looks fine to me, the cut you can glue down with some rubber cement or any glue that won't go hard.
You may resurface it with some abrasive paper if you feel it's needed....

My favorite strop is a horse hide from 1929, it's still as good as new, so they can last a long time.
If you find it not to be of any use for stropping, get some good oil on it to preserve it and...