If you have to splice a new connector or contact on to the harness, then take care to make sure that the spliced wires have a good electrical and mechanical connection. Spend some time verifying what wire goes to what contact hole in the connector. Mark the wire so that when you cut the old contact off you know to what connector hole it goes (the remaining wire on the harness is what should have the mark, not the piece in you hand).
Before you get started replacing the contact be sure to put some heat shrink tube in place on the harness side of the remaining wire. I prefer this to electrical tape.
The best way I have found to have a good electrical and mechanical connection is to use an uninsulated butt splice and then solder it. Install heatshrink and if possible use a heat gun to shrink the tube (preferred method).
NOTE: DO NOT USE ACID CORE SOLDER.