What about a triple beam setup? The individual beams would be only half or a third as powerful, making them safer to human eyes. Only where they cross they would carry enough power to zap the mosquito...
This laser is 200 times too powerful to be considered "mostly safe" for human ayes (cat 3R) and 1000 times too powerful to be considered safe (cat 2). I toyed with the idea but it's hazardous in any usable setup. If you'd like to do it moderately safe I'd stay away from lasers. Use a power LED and parabolic reflector to make the beam as incoherent as possible and then focus it with optics to create very narrow focal…
Thank you for your thoughtful explanation.