1mm cable should be OK but it is available with more flexibility. The 1mm sold by 'Vehicle Wiring Products' is 32 strand.
I measured my original harness and came up with (approx) 1.5mm used on all wiring except 2.0mm used for battery to ammeter, rear lamp to switch and then rather strangely from the main switch to the connector close to the 'A' terminal of the regulator (the last bit was 1.5mm !)
In the end, these were a bit small on the OD as modern pvc insulation is thinner than the old rubber so I used 2mm / 28 strand for general wiring and 3mm / 44 strand for the heavy duty bits.
More strands would have been nice but I have nice bright lights !