Removing old solder when replacing speaker

I broke the blue and red wires when replacing the screen, The red one broke off the board and the blue one didn't. The wires are still sticking out enough on the speaker to use them. My question is do I need to desolder the solder from the board it connects to? Someone mentioned in another post that you can solder these wires to the top of the board instead of the bottom where it previously was. There are two gold contacts on the top of the board directly on the opposite side of where it previously was soldered to. I know the solder is conductive but is it okay if i solder the wires on top of the old solder?

Thanks in advance!