You mean a negative combat sensor ability?
I thought AIs were the only ones who put minesweepers on warships anyways (since they can't balance fleets)
As far as I know, all of the gnarled veterans simply make:
A stack of N dedicated minesweepers (N = max mine stack / number of mines swept per sweeper) plus a set of M warships (where M approaches infinity)
Dedicated sweepers don't need shields guns or armor, so they are far more efficient. And the warships get to use all their tonnage on guns and shields.
And critically important, you're not wasting any tonnage on superfluous sweepers if you add more ships to the fleet.
Think of my "remove minesweeper ability" suggestion as making minesweepers be "destroyed on use", with the bonus of protecting against direct fire too.
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