https://panopticlick.eff.org/ reports that 1 in 1.67 browsers send the DNT header, so the best option fingerprinting-wise might be to leave it on, at least information-wise.
Sorry, I left that part out. My browser sends DNT=1, and I get 1/1.67, which should mean that 1/1.67 browsers send DNT=1. This means that the total share of browsers that send the DNT header at all is at least 1/1.67, but probably higher.