Is it safe to use a cheater plug with a two-prong extension cord?

Not really safe, and definitely not worth the risk. A cheater plug only works if the metal tab is screwed into the outlet’s cover plate, and even then the ground connection is flimsy. Two-prong cords have no ground wire, so any fault could make the tool’s metal case live. If you need grounding, buy a grounded three-prong extension cord instead.