I've been using a small square of chainmail to clean my grill (and occasionally my cast iron pans) and follow it up with a damp paper towel It works well but is kind of a PITA compared to a wire brush.
Every cleaning solution that doesn't include a surfactant is worse. It's slower, more labor, intensive, more water-intensive, and it leaves baked-on crud behind. The latter two are both much worse for cast iron than soap.