What PCB is needed?
The Crazy Kong to Nintendo edge adapter is specifically for single PCB Falcon-style Crazy Kong boards. They have a 36 pin edge connector. Clones or copies of Falcon's Crazy Kong board should work too.
Other kinds of Crazy Kong boards have different edge pinouts, including the two PCB Falcon boardsets.
The Multi Crazy Kong/Crazy Kong Remix kit on the other hand should work on pretty much any *normal* Crazy Kong board - Falcon, Orca, etc... ...as long as it isn't a bootleg of a bootleg (eg: actually bootleg Galaxian or Scramble hardware)
This kit though, expects Crazy Kong Part II color PROMs to be present. If you have green girders or something else unusual, the game ought to run but who knows what colors you'll get.
And lastly, the kit plugs into the Z80 socket on your Crazy Kong PCB. Some boards have their Z80 soldered directly to the board. If your board has a soldered Z80, you will need to desolder it and solder in a 40 pin socket.