The only thing wrong with stropping on your hand is that you have to have no dirt on your hand and you also need to make sure any filth that comes off of the iron (swarf, etc) doesn't end up on a project because you stropped it onto your hand.
To that end, having hard oiled leather on a hard board might be better (but then you have to keep that clean).
I doubt anyone on here has bought more sharpening media to play with than I have. It doesn't really matter what you use - you can have expensive coarse and fine media or cheap coarse and fine media and they all work about equally as well. For $10, you can match a shapton 30k and not worry about breaking it and for about $30, you can get the best bevel grinding stone ever made (the norton medium crystolon) and install it in some makeshift oilbath to be used with light mineral oil.
But, what's not often given as advice is to spend $15 on a cheap USB hand held microscope and see what's happening at the very edge of your tool. It's as cheap as a loupe, far more useful, and you'll only need to use it a couple of times to sort things out. In all of the stuff people will tell you about steels or sharpening media or burrs or whatever else, you'll find almost without exception that if you have a problem with sharpness, you didn't get the fine stuff to the very edge of the tool and finish the job.
Here's why the $15 is worth it - it takes very little effort to finish the job, but you can find yourself methods where you do a whole bunch of work to get close to the edge and then manage to do a little working the edge itself and start to think that all of it was important. It's not. There's setup work (which never needs to be done by the fine media) and finishing the very edge. Literally thousandths of it and no more. Understanding this will make sharpening all kinds of things freehand a lot easier.