In my first try, it didn't work, because my Scuttler was H/H, and had more health than the Skitterling even after taking the first damage, and so was swapped in again, but really that first pet doesn't do anything but take the hit, so I suggest that you can use anything, as long as it will be lower health than the Skitterling after the hit. (edited)
With BfA Pets, you can replace Gulp Froglet with either Coastal Scuttler (mine was H/H) *1* or Elusive Skimmer (*2*). I just tried this with a P/S Elusive Skimmer, and my Gahz'rooki still had more health than it did, so the Skimmer might not be viable, but at least the H/H Scuttler worked!
This doesn't work at all for me. On Rd 2 he hits my left shark for 1192, and on Rd 3 he kills my shark with slicing wind before he gets off dazzling dance. I tried it several times - has this strategy been nerfed?
My Ghazrooki was swapped in before shark so instead of the second pass round I just switched to shark and followed strat as writen after that, but like others took a second bite but at least he died without any rng