It's most likely the rope is TIED to a thimbled eye on the wire.... The only way you can remove the halyard is to take exit box out at the mast base. You'll need to clip the thimbled eye off the wire's shackle end and securely tape a messenger line so you can pull the wire through the mast head sheave.
You can use the messenger line to pull the new halyard through and up the mast.
There are pre made wire/rope replacement halyards available... they are splice so the connection will pass through the base's exit box.
Many have converted to all rope halyards.... just make sure the masthead sheaves will accommodate it
Or you can buy or build a "tapered" halyard... which is a line with high tech core that as the cover stripped off where it isn't needed for handling or cleating. Check out this link for splicing and rigging ideas.
http://www.apsltd.com/c-1539-splicingservices-halyardssheetsguys.aspx
I made my halyards by covering high tech Amsteel 12 core with an inexpensive polyester cover. I added a "luggage tag" eye splice to single braid Amsteel for the shackle. It's cheaper to buy the core and add a cover than it is to purchase high tech double braid, like Samson Warpspeed, an strip the cover off.