6mm x 16mm can't be standalone so there must be some sort of connector off the board to other circuits. Can 3 pins be added to the connector? i.e. basically what Mark has said.

Beds of nails really need locating holes too. If you have enough space for the holes, that's the way.

If cost is so sensitive that a small connector is unfeasible, then I'm assuming high volume. High volume would exclude soldering wires to the board.

From the sort of vague description it would appear a bed of nails is the only option, possibly with a guide outside the board if no space for guid holes is available.