Q: What is the safest way to clean soiled concrete for tiling in a small kitchen?
I'd go with a decoupling membrane - like ditra.  The membrane technically requires the substrate to be clean for bonding as well but the failure is less likely for the whole membrane vs a single tile.  If you bond the membrane to the floor using the recommended thinset and then bond the tiles to the membrane the tiles will be held tight.  If the membrane bond isn't perfect that shouldn't really matter as it will move as a whole and derive strength from the overall bond and weight of the tile on top of it.

I'd still scrape the concrete with a floor scraper.  I don't know if I'd do much more than that.

You could grind but as you mention it can be dusty and expensive.