I found some pics online. Man, those are some tiny ships!
If it was me, I'd paint the hulls before the sails. For the sails, maybe paint them in white or very light gray, then hit them with a brown wash (maybe GW's Agrax Earthshade or Seraphim Sepia). That would bring out the details and make them "dirty" as you were describing.
But yeah, at that scale, I'd highly recommend thinning down your paints. Will be very easy even with acrylics to cover up details with the paint.