Ah that team...
Well here is a couple of things I like to use.
S/S Sky-Bo, as you already tried. Decoy will block Cyclone or Thunderbolt AoE. Of course your oppoent will get wise to it, so after a few fights when they have learned their leasson it will become a mindgame when to use Decoy. Also helps that Sky-Bo has strong vs Mechanicals attack.
S/S Prairie Mouse. Flurry will remove Decoys fast and hurt Blighthawk alot. Being critter takes less damage from Thunderbolt. Poison Fang DoT is strong vs Mechanicals which is excellent when they switch away the MPD. Then you can either go for more survival with Survial or more damage with Stampede. (stampede buffed poison fang dots really destroys MPDs).
Pandaren Fire Spirit. I run it with Magma Wave, Flamethrower, Conflagrate. Magma Wave is excellent at removing Decoys and Cyclones. Never be afraid to use Conflagrate without the burning buff and then switch away to another pet. The problem/risk with this pet is of course the Jademist Dance, so you really must avoid that match-up.
Tideskipper. This is more safe vs the Jademist Dancer than the Fire Spirit and will take weak damage from the Blighthawk unless runs with Slicing Winds. Crush, Tidal Wave and either Clobber or Geyser. Clobber can be nice against the Blighthawk. Geyser is better against the MPD. Tidal Wave of course removes Cyclone/Decoy.
S/S Qiraji Guardling. Can be dangerous to use when facing a Blighthawk if you get hit by the powerful undead attacks. But with Sandstorm it nullifies Cyclone damage. And it is just excellent against Jademist Dancer. Wait for them to use Rain Dance then use Blackout Kick and Sandstorm, this will make them lose both turns of the buff, except for the Cyclone if that is up.
Voodoo Figurine. DoT up your opponents(or dot+wild magic), since Clonedancers like to switch around alot. Sear Magic to remove the Cyclone. Possibilty of strong attacks vs the MPD and will take weak damage from MPD basic attack.
Vengeful Porcupette. This one can kill blighthawks pretty fast, works decently against MPD and quite well against Jademist Dancers, just have to make good use of Spirit Spikes. It won't save your team from the Cyclone though.
S/S Grassland Cottontail. Excellent annoying 325 speed 260 Power pet. While this one also won't save you from the Cyclone it will sure punish all/any of those three pets.
S/S Highlands Skunk. Flurry to take out decoy/blighthawk. Bleat for AoE heal to lessen cyclone impact, or Stench for hit-debuff against cyclone and other pets.