That's not how radiation exposure works. The types of mutations in DNA it causes is generally things like cancer, not birth defects that transfer into future generations. In order for the number of fingers human-wide to change, there would need to be a specific mutation for that, and that mutation would have to be beneficial enough that the 11+ or 9- fingered folks would be more likely to breed than us 10 fingered folks.
On top of that, while base 10 is convenient because of our fingers, it's unlikely to change due to how ingrained it is in our culture at this point. It's also hardly the only system we've used. The Babylonians used a base 60. Many cultures have used base 12. Base 12 is actually very convenient for our fingers already.
Hold your left thumb against the first segment of your left pinky and count 1, move up one segment, count two. Count each of the segments on your left fingers. You're now at 12. Move your right thumb to the first segment on your right pinky, and then start over on your left. Each time you count 12 on the left, move your right thumb up one. You can now count to 144 on your fingers.