No diode is needed for the situation you described.
It is, however, recommended to wire a diode parallel to the relay's coil that would be in reverse of positive/negative. (Positive) --|<|-- (Ground).
I am not sure what the current is on the remote wire you're asking about, if it is enough to keep a relay powered, without burning anything. Read what the current rating for it is.
Why not simply find an ACC wire and use that? Your radio should have one coming into it. Those are usually 10Amp + rated.
I am not sure about the relay wire numbers, as I am used to seeing them on diagrams.