It is really hard to guess this number, but here is a statistic that might be useful: It appears that there are less than 10,000 people who have solved a cube blindfolded in an official WCA competition. I'm not sure of the exact number because I don't have a recent WCA database dump downloaded, and the statistics page has been limited due to the size of the database getting too big. But I have found that Hideaki Tomoyori (友寄英哲) has gotten a 3x3x3 BLD solve in competition (at over 80 years of age!) in 13 minutes and 55 seconds, and he is ranked 7865 in the world. So I would guess the total number solving in an official WCA competition is likely somewhere around 8000.
It is hard to guess what percentage of people who have solved a cube blindfolded have done so officially. I would guess it might actually be a fairly high percentage, since anyone with the dedication to try to solve a cube blindfolded is likely to want to prove it in competition. But what I'm considering a high percentage here is still far less than 100% - if I had to guess, I might guess that 10% of people who have solved a cube blindfolded have done so in official competition?
With that assumption, it seems reasonable to guess that perhaps 100,000 people have solved a cube blindfolded. But that is certainly a very rough guess, and could potentially be off by a couple of orders of magnitude.
