Here is a short video on youtube showing spiral binding. At the very end, he shows how to cut the binding and crimp it so that it doesn't come out of the holes.
How To Spiral Bind Papers - YouTube
It looks like you could do it with a small pair of pliers, but I'm sure there is probably a special "crimping" tool, because there is a tool for everything, lol.
Take a look at a regular spiral notebook. The end of the spiral wire is just bent back into the coil.
Hope this works. I'll bet your little son loves the book you made!