Polarity IS important. If you get the polarity wrong your speakers will cancel each other out as some frequencies because they are interfering with each other rather than working together.
Solder is always the best way to join wires. But I think that crimp on splice connectors would be OK for this. The wire is small diameter so there can't be much current.
Thanks for your advice. I followed the wires coming out of the connector and matched them to the new connector so the speakers would not cancel each other out. I cut the wires and spiced in the new connector with just electrical tape. I think your right solder would be an overkill for this wire. The whole process only took about 5 minutes and it sounds great again. Thanks again.