I know of NO appeal against capital punishment that is being conducted without the very explicit consent, endorsement and participation of the death row inmate themselves. Care to show me one?

I draw a distinction between appeals for a particular prisoner and the broader appeal to do away with the death penalty entirely. It's the latter where I am not aware of any organized effort by the prisoners themselves. The movement will sometimes mention a particular man who was innocent or for some reason the penalty seems especially unfair. But not the average guy where there is little question that he committed a terrible crime.

If that is not just a politically correct way to say "STFU" what is it?

It's an argument that saying those things will have an effect in the world that we don't want. It's not based on the fact that I personally disagree with them. People who don't agree with my judgments about the effect in the world or don't care won't see any reason to follow the advice. That seems very different from STFU.