Have you considered changing the plugs/receptacles?
240V stuff costs more, so changing the ends may be cheaper.

Is the wiring normally used for 120v sufficient for 240v use?

The short answer is Yes. 240v in a cable is supplied by 2 wires (plus a
ground). Each "hot" wire carries 120v. By switching ends, you are making the
neutral (white) wire function as the other hot (red) wire. 240v motors do
not require a neutral.

Just as with a 120v extension cord, the current draw of the tool, and length
of the cord determines how heavy a cord (wire guage) is required.

-Steve