Definitely don't plug it in as-is. Bear in mind that although the transformer is rated for 120/240V, other line-voltage items such as the switch, power cable, fuse and any filter capacitors might not be. Different parts are sometimes fitted depending on the voltage for which the unit is configured during manufacture.
If all are OK for 230V, then as far as the transformer taps are concerned, it looks like the white lead is 120V and the red 240V, while the black is common to both voltages and contains the thermal cutout. If the red lead is currently insulated (e.g. terminated somewhere with no other cable connected, or sleeved over) it would be a matter of connecting red in place of white and insulating the white lead. If there is an internal fuse, it may need to be changed (to one of a lower current rating and suitable voltage rating.) For safety, the insulation of the appliance should be tested on completion of the work.
I would also then check for correct output from the transformer secondaries before use, in case all is not what it seems, e.g. if the label does not match the real colour code of the leads as is quite common. In fact, on the bench, I would validate the procedure before starting, by running it from 120V as-is and checking for 240V across red and black.
All in all, it might be easier and safer to get a small step-down transformer, as the load can't be very high. Just don't buy a firecracker from some unknown grey importer!
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