Mulligans
General Mulligans
Don't keep Feign Death early in the game unless you're sure your main minions with deathrattle will not be destroyed early, as you will probably not have enough mana to cast Feign Death. You should be dropping more minions on the curve in the early game.
Hunter's Mark or Freezing Trap might help you establish tempo in the early game so you can consider these, but will definitely have more value against decks with single large minions or buffed minions. Thus mid to late game would be where these cards shine.
Before most of the good deathrattle minions get rotated out, stick them together in a deck with Undertaker, Feign Death and Kel’Thuzad for some fun!
This deck plays like tempo, so try to mulligan for a good mana curve at the start. Against decks where you know you will be facing single big minions, aim to get a hunter’s mark or freezing trap in your hand.
Synergies:
1) Feign Death + EVERYTHING
For board presence: Haunted Creeper + Harvest Goelm + Piloted Shredder + Sludge Belcher + Cairne Bloodhoff + Piloted Sky Golem + Savannah Highmane
For card draw: Loot Hoarder
For stealing enemy minions: Sylvanas
The dream: Having Feugen or Stalagg destroyed first, then dropping the other one, and then using Feign Death to proc a free Thaddius.
2) Kel’Thuzad
Gets more bang for buck out of your deathrattle minions that may now be used as suicide machines.
3) Baron Rivendare
Also gets more bang for buck out of your deathrattle minions by having them proc twice.
4) Cult Master
Having so many minions on the board, hopefully mostly from Haunted Creeper and the Harvest Golem at the start, will let you reload your hand if you drop a Cult Master and run your minions into theirs.