Umm, unless it's for the pure purpose of burr removal, a strop won't do much after a 4k stone.
Most of the stropping compounds are akin to a 20,000+ grit edge, so making that large of a leap doesn't do much.
I would definitely want a stone between the 4k and the loaded strop.....an 8k GlassStone if you're liking them.
An 8k GlassStone will provide a wicked sharp edge.
If it were me, and forgive me but I'm not a huge strop person, I'd get this set:http://www.chefknivestogo.com/habastset.html