Is it safe to use a cheater plug?

No, it is not safe to use a cheater plug in the way most people do. The ground prong exists to direct current safely to earth if something goes wrong, but a cheater plug only works if you connect its metal tab to a properly grounded wall screw. Most people skip that step, leaving the tool ungrounded and creating a false sense of safety. Just buy a proper three-prong extension cord or have an electrician replace the outlet — your safety is not worth saving five bucks.