another option?
ingredients:
- pen/pencil for writing: 1
- paper to write on: as much as rquired
- 16-sided hexadecimal dice: 1
- an even ground to roll the dice 64 times: as big as possible!
congratulations you now own a private key. not to get your bitcoin address you need:
- some tool to convert the hexadecimal result to a bitcoin address.
- a DVD with live linux to run that tool
now you are only trusting ECDSA and hashes to be safe.

There are no 16-faced Platonic solids. The only games in town are: tetra-hedron, cube, decahedron, do-decahedron, and icosahedron, which have four, six, ten, twelve, and twenty-sides respectively.
You may have other shapes with exactly 16-faces but it will mean there will be a bias to some outcomes more than others. You could use a 20-sided die and mark four of them as "re-roll".