Have the mission be offered by the përs ship, and flag it to replace the special ship with the përs.
You can make the përs appear under specific circumstances if required by setting it to appear in certain systems a fixed percent of the time, and only appear if a certain logical string evaluates to true.
If you want the mission to be offered from a planet, just include something in the description to the effect of “Go to XYZ system and hail the <përs name>, then <whatever else>”.
If the përs cannot be hailed, make a special copy of it that can be hailed, use that for the mission, and set the normal version to not appear when the mission is going.
If you really really don’t want the përs to be hailed nor boarded nor disabled, then I think you’re going to have to make a shïp that’s identical to the përs (this is what EV Override did for the mission to hunt down The Nadir—there is a shïp called The Nadir, which incidentally with a purchase price of 40,000,000 credits is the most expensive in EVO, meaning if you capture it you can kit out your ship to achieve the highest possible trade-in value in EVO) and stick it in a düde that never appears except for the mission.