Is it safe to use a non-polarized extension cord with a polarized plug?

No, it’s not safe. A polarized plug has one wider blade to ensure hot and neutral wires connect correctly, but a non-polarized cord lets you plug it in either way — and if reversed, the device’s switch and internal wiring may stay live even when off, risking shock from exposed metal parts. The hazard is real, especially in damp areas or with metal-bodied tools. Don’t save a few bucks here; get a polarized extension cord, and grounded if the device has a three-prong plug.