I would advise caution when using power tools in wet or damp conditions. Being double-insulated does not necessarily provide better protection (under wet or damp conditions) versus a Class I earthed appliance.
Best to consult the user manual for advice; otherwise as a minimum I would recommend the power tool is connected via a Residual Current Circuit Breaker (or earth leakage device) which will cut the power should the worst occur. Of course all modern homes will be fitted with an RCCB within the distribution unit – so check before wasting money on an unnecessary device.