I can tell you from personal experience, the grit contamination at that level is negligable. You can SEE the particles easily at 150x and lower, so if it's got stuff stuck in it that is bigger than that(which it won't), just rinse it off with a brush. If a brush won't take it out, then return the stone, because you are going to be abrading knife steels on it, and that is going to be way worse for loading up a stone than a sidewalk. Concrete is not lower grit than 150x, and if it were, I'd be sharpening on it. What you are doing is really just abrading down the cement over a large area with your coarse stone, but the sidewalk(or whatever) is so big, you end up wearing the stone down evenly without much technique.
Just to belabor the point, this is not some newfangled or outlandish idea--it is how you polish a concrete floor. There are machines that have little segments on pads that abrade the floor starting at 16 grit or so and shine it up until it looks like it's covered in wax. All you are doing is using the stone to polish the sidewalk, but you rub it on a large enough area that the general flatness of the sidewalk wears down the high spots on your stone.http://www.concretenetwork.com/concrete ... evels.htmlhttp://www.icpsc365.com/industry-inform ... d-segment/
All they suggest for glazed abrasives is adding water--that's right, this polishing is done DRY. Your stones, which are both used with water and have MUCH softer binders than these polishing segments, will not have this problem.
I discovered this discipline myself because I flattened a piece of concrete with the 120 grit stone and realized that I'd just worn down the concrete to 120 grit finish and it was pretty smooth. So I put my 500 grit on it. Then my 1k, then my 2k. All the stones were perfectly fine, flat and fresh looking, and that ledge has a very smooth spot on it to this day.