The best solution is to replace the cable assembly (part of bottom case) or at least splice in a replacement connector.
[https://www.thebookyard.com/product.php?cPath=96_217&products_id=11314|Mac Mini Housing - Bottom (09)]
[https://www.thebookyard.com/product.php?cPath=96_97&products_id=13741|Mac Mini Power Button Kit (06/07)]