I found the easiest way to compress the springs is by hand with a zip tie or cable tie (depending where you are from 
) Put the zip tie around the spring and then as you wind it up you can pull the tie closed with your teeth. Just make sure the bulky part of the tie is not going to interfere with anything when you put the clock back together. I have done quite a few alarm clocks in this way.
Good luck and let us know how it goes
Paul.
