You should still be able to use the existing wires, capacitors (and even the jack, although it won't be connected to a battery any more).
But since you'll be disconnecting almost everything, it might be easier to do a fresh rewire using the new pots.
You'll also need a ground/earth wire from the bridge/tailpiece to the back of a pot - there may not be one already because EMGs don't need one.
For leg length, EMGs have short legs so you probably want short (1/4") legs, but long (1/2") would probably also fit unless the pickup cavities are very shallow. Either way, I'd go 1/4".