For the sake of safety, I would definitely replace the old line cord with a three-wire cord. If you sell the radio someday, advertise it an an "upgrade", not a "modification". If the buyer is a so-called collector who is willing to pay more for a radio in original condition, charge an extra $100 and send the old cracked, frayed, dangerous line cord with the radio so he can reinstall it. :-)
73,
Craig
W3CRR
