I found the answer in this thread, but because the pictures are missing and they would have been helpful, I'm posting a similar version with illustrations. (And I chose this StackExchange site since that thread is on a bike website and these watches serve to count bike speed.)
I used an X-acto knife to cut around the Polar logo at the front:
I cut to around 1cm depth. The knife seemed to reach the end of the thickness around the middle, so I used a screwdriver to lift it:
And here is the result:
I removed more material from the edges so the battery could come out, and slid the x-acto knife below the battery so I could force it out with the screwdriver:
The battery is a CR2354 3V, wider at the base:
It is indeed empty. I'll order a new one, add padding to ensure electrical connection, then wrap it with electrical tape. If I need it underwater, I'll add silicone sealing.