Without the original plug intact it's impossible to see which was the center pin and which was the body.
With some electronics knowledge it is easy to tell by following the copper traces on the board but if you are unfamiliar with circuit boards it might be difficult. I suggest you buy a testmeter, it can be any model and they cost just a few Euros. It doesn't have to be a digital one, a needle on a dial works just as well. You set the meter to measure resistance (Ohms) and place one of the probes on the metal shell around the USB connector. Place the other probe on each of the three solder joints under the DC socket in turn. The one that make the meter read zero (or the needle goes all the way across if it's an analog meter) is the negative connection.
You will do no damage by connecting the positive wire to either of the other joints so you can try both, do it with batteries removed in case you feed power to them instead of the clock. One will work as expected, the other probably won't work at all although I can't be certain without seeing it.
Now you have to find out which of the wires from the wall adapter is positive and which is negative. To do this, change the setting on the testmeter to measure voltage and select the lowest range that is higher than 5V (10V for example but meters vary). Make sure the black probe wire is in the negative meter socket then connect one of the probes to each wire. If the meter reads about 5V you have the probes the right way around so you have found the polarity. If the meter reads -5V or the needle goes backwards the probes are the wrong way around and you have the negative probe to the positive supply and vice versa.
Once you know the polarity of the adapter wires and which is the negative solder pad on the DC socket, all you have to do is wire negative to negative and positive to positive.
Brian.