Daniel,
Do not toss out your strop after you get your Shapton.. 3-4 strokes on the strop might/will still improve the initial sharpness. My question is, how fast does any such difference disappear with planing. Maybe I will experiment one day.
For fewer $$, try a pinch of 1 micron diamond powder on some soft steel from a hardware store. Cast iron is being recommended (Derek Cohen has a useful post on his site). I tried both (cast and steel) and they seem to work the same and rather well.
Best wishes,
Metod