Unlikely to be a CR2032. They are HUGE, size of a quarter. I wrote this Tip.
Changing Watch Batteries
Lots of posters ask "what is the battery in my (name of watch)" with a view to changing it yourself. This is a bad idea for many reasons. You don't have the tools or knowledge to remove a rotary screw on back, or the gasket sealant for a waterproof watch. Some fashion watches have 4 traditional screw and need professional grade jeweler screwdrivers
. Also, there are about 20 batteries commonly used in watches, in various sizes and internal technology, Lithium Ion, Silver Oxide and Manganese Alkaline. If you buy them, you generally have to buy 10!
Don't sweat the details. Just take the watch to your local jeweler. They have all the batteries at hand and the tools to remove the back. It is done whilst you wait for $8 to $15!