Youch! You're braver than I am.
Looking at the plug, it may well be that it dates from the days of AC/DC mains. I really wouldn't risk of powering it from the mains today. You have no idea about the quality / deterioration of the insulation (coil primary-secondary), that capacitor may blow up unexpectedly (and probably spectacularly!), no fusing, cable strain relief etc.
In all conscience, I really think it really is one for the 'curiosity display' rather than being plugged into the mains.
It probably wouldn't be too difficult these days to build a small high frequency inverter to safely drive the wands.
Edit: Anyone else notice the slightly dodgy sounding product logo!