I dried out a watch once by taking the back off, the battery out, and leaving it open-side-up on the dash of my car on a hot day. Worked a treat!
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson
The battery voltage of the cateye is low enough that it wil not be enough to damage the elctronics. The LCD display is sensitive to heat and can be damaged so if you use a hairdryer, keep the dryer away from the display. If the display gets too hot to touch, you may damage th display.
Also remove the battery ASAP while it is drying out.
smilingcat