If the strain relief itself is intact you can remove it.
Trim the in housing plastic and wires close to relief, then vice/clamp the strain relief or just hold with a rubber glove and spin the wire exiting the relive, always rotating in the same direction (8 inches cord works well). It takes a bit of force but I have done it many times and it works every time. Once out you can slide new wire in, use zip ties, hot glue, clamp, silicone (your choice) on the inside of the housing to re-secure the cable. Don't rely on the strain relief to hold the cable in place that's not what it's for.