Add iPod 4 dock to old Hi-Fi (Will my idea work?)
This is essentially correct. Two things though.

One, you should make sure the vcc you are tapping, which you said is ~4.83v, is regulated.

Two, you should make sure that you have enough headroom to actually use that 4.83v line. The 2.8v/2.0v signaling indicates to the iPod that it can draw up to 1 AMP of current. That may be more than the hifi can spare or is designed for, on top of what it already pulls. You might need a bigger power supply, a better regulator, or add a heatsink/cooling on the existing one. If it regulates down from a higher voltage, say 9v or 12v, you could add a second regulator just for the iPod and replace the power supply (Assuming it is an external ac to dc power adaptor. If it is an internal one, way more complicated).

Even the 500mA charging mode might be too much. Just a heads up.

Also, pin 21, you could connect a 1k resistor to ground for Dock mode, but sometimes if the dock has no controls, you really can't use it for anything. An alternative is using a 66k resistor to ground. This puts it in line-out mode, where it uses the dock connecter for audio instead of the headphone connector. You could test both before finishing to see which one you prefer.