Make the bundle by winding the wire 32 times around two spaced pegs so as to be certain that all the 64 wires this produces between the pegs are parallel and not intertwined. Slip the wire off the pegs and do not twist it, but squeeze the parallel section so that it takes up a cylindrical shape.
Wrap another length of the same wire tightly around the outside of the cylindrical section for a known number of turns (20 at least). Unwind the wire and measure its length and divide by 20 to calculate the mean circumference of one turn.
Do exactly the same thing with a length of wire whose diameter you do know (probably something much larger, so that you can measure it easily). You may not be able to wrap as many as 20 turns, so adjust the divisor accordingly.
The ratio of the lengths of the one-turn circumferences will be the square of the ratio of the wire diameters.