Certain sensor wires are shielded to prevent interference they normally have a woven type strand around the inner wires that is earthed at one end.
The "wire" as you refer to it, does not actually do anything signal wise to the ecu, apart from obviously ensuring the others signals are not contaminated.
In the std way the loom is routed the replacement of the connector will not pick up interference and will be fine, the braided shield does not pass from the one side of the connector to the other anyway.
tabetha