There may be a way to splice a new connector on the end or perform other
micro-surgery on the wire, or perhaps obtain another wire like that from a
different portable model G4 iBook or PowerBook where the airport card
was a separate component, to use to replace the one defective one...
https://www.ifixit.com/Device/Mac_Laptop
Not sure if there are any DIY fixit pages posted online; and have not checked
the http://ifixit.com repair guides for portable Apple computers, to see if they
happen to have a reference to fixing just the cable. The full cable replacement
may be rather involved, if you choose to actually install a complete new wire.
A company such as powerbookmedic may have replacement cables. Or a call
to wegenermedia could also be helpful, if you were considering other upgrade
services and sought to include this repair in the mix, whilst the repair center
had the iBook open. These things cost less in conjunction with other repairs
since once an iBookG4 is open, most of access problems are out of the way.
The later iBook G4 has the wi-fi and BT card attached to the bottom of the
logic board, though replaceable much more takeapart is required for access.
Hopefully you can replace or splice the wire to fix this problem.
An authorized service provider may have ideas, too.
Good luck & happy computing! 🙂