I know nothing about iPods, but when I send my MP3 player’s FM output into the T-amp sitting on top of those stereo speakers over there, it sounds as good as a normal radio receiver, to my ears. Do you want to end up with vintage sound, or with vintage looks and modern sound?
You could put a little t-amp inside the radio cabinet, bypassing the original circuitry inside the radio, replace the speaker with a same size modern one with appropriate specs, and end up with decent mono sound.
The hard part (for me), with an old cabinet, is matching a new midwoofer, tweeter and crossover to the cabinet. There’s something called the Emerald City Do It Yourself Speaker Contest, or something. You want to find one of those people. Wait a sec… here you go. Whatever you have in mind, ask these people.
The Puget Sound! DIY Speaker Contest
Pacific Northwest Audio Society