I have 30mm wooden venetian blinds and wondered how people clean them. I just use a duster and then close the the other way and dust again. This works ok but there is a narrow layer which is hidden when they are closed hence a little dust.
But it is only dust and not grimy. I have one of those dusters that clip on and clean both sides at once but i have not the patience. I honestly do not see anything tho that would require heavy cleaning and they are up over a year, just dust.
Also wooden cannot be washed in bath and i could not take them down anyway. i love them tho and want to keep them as clean as poss