Yep, that was exactly what I was talking about.
I had a custom-made one, using a very aggressive blade angle specifically for thick hair...problem was he retired and my blade broke during a move. There is a trick to them, it's not hard at all, you just gotta pay attention.
As far as the strop (the actual name for that strap), all it ddoes is straighten the blade edge as it bends...the edge on the large ones are so thin they bend. There are small razors which don't need stropping, but their blade profiles aren't as nice as the big ones, and I've never seen one get even close to as sharp as a poorly sharpened full-size razor.