Nah - it's not difficult, and you don't need a fancy digital soldering station - although if you have one, by all means use it - any $20 soldering iron will handle it.

There's probably a little stub of wire still in the hole (makes it easy to identify) - heat the pad until the solder melts and then grab the stub with needle nose pliers and pull it out and then stick the "new" wire through the solder whilst it's still molten.

At this point, the clock is already not working so you can only break it more. 

fordem had the right trick though, just heat it up and go for it.

Soldered the wires back on and presto, it works.

But the light bulb is blown out, lol.  oh well

Good to hear you're making progress - I'm pretty sure if you fix the broken wires you can replace the bulb.  I've never seen that particular clock, but the one in my Swift takes a regular bulb behind it.

I'm pretty sure it is just a small bulb that you can get at an auto parts store.  Just take the old one out and match it up.  You might be able to read a number on the old bulb, but if not just get one that looks the same.