My fence has gone green, so should I use a green coloured product to overpaint this?

NO, before long that algae will soon come back and ruin your hard work.  It is best to remove the algae before you paint and the final results will last much longer.  Spray on the Bird Brand Fungicidal Algae Killer and within a day or so, the green will disappear and then you can paint the colour you want.