I just remove the IC and stir with a sanitized spoon to whirlpool.
But if you want to build something go for it.
I'd actually like to have the whirlpool to speed up the chilling process. Like you said, for the hop cone, a spoon does just fine.
Recirculating the wort with a March pump has cut my cooling times by more than half. Definitely recommended for the chill, but I don't use it to whirlpool.
I still use an IC, so I do what Mort described above (chill, pull IC, whirlpool, let stand for 15 min, run off).
I have a Street 90 elbow that faces down on my kettle outlet, and I dont need a scrubbie/filter to get clear beer, even with IPAs. I don't get a perfect cone, but all the trub settles around the elbow and only the first bit of liquid out of the valve has trub in it. The rest comes out clear.