It is most likely to be centre positive I think, but you really need to know for sure. Like Graham says, look on the power adapter for voltage / polarity (or maybe on a sticker on the clock itself). If the wires are two colours, voltmeter on them to find out which one is positive, then look at where they go into the plug, and use the continuity checker on the voltmeter to find out which one goes to the centre.
Once you’ve found out the details, easiest thing to do is just go to maplin and buy one of the right voltage, and make sure you set the polarity correctly. Easier than soldering the wires back, and cheapish. Although if you’re okay at soldering and have soldering kit handy, and a voltmeter to find which wire is which, you could fix it pretty quick.
By the way – probably just how you’re wording it, but you are just fixing the wires between the power adapter and the clock, not doing anything with mains power / wiring your own plug on right?
Joe