Mulligan tips translated by glormagic:

Always keep: Filletfighter, Buccaneer, Parachute Brigand.

Other situations:

Keep only one Swordfish or Cavern Shinyfinder.

Keep Cavern Shinyfinder when going first.

Keep Swordfish when going second.

VS Aggro: Keep Ship's Cannon, Prize Plunderer, Pufferfist.

Always keep at least one 1 mana Pirate except Patches.

If you have one 1 mana Pirate, keep one Secret Passage.

If you have 1 mana Pirate but don't have Cavern Shinyfinder when going first, keep Amalgam.

Keep Dread Corsair when you have Shinyfinder or Swordfish.