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...
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 depth. Then it will still be able to burn the mosquito but won't be a blinding hazard as little as 20 centimetres from the focal point.
Thank you for your thoughtful explanation.
(And Australia’s laws here were decided based on safety standards, the figures of which uuidgen points out.)