It would work! A cr2032 is a super common "coin cell" battery that we use for all kinds of stuff.

The "problem" with this is how long it will run for. A watch battery, or a coin cell doesn't have much current capacity.

You can also get specifically low powered attiny chips as well, so a cr2032 would be more than sufficent to power it for a number of months.

If you look at the picture below "Made in Oslo".. you'll see a cr2032 battery.