I estimate that less that 100 mW total will be required and all moving parts will be mechanically isolated... Simple enough to do with some foam and silicone based adhesives... Further If both the x and y axes are fed the same linear ramp signal, properly phased... the Red Laser diode could be pulsed on/off for a 'Vector Display'[ device... great for displaying text too...
Can't be done in the manner you are thinking of, namely you are trying to build an "open-loop" system, with no feedback on position.
If you want to go beyond simple lissajous (sp?) figures, and be able to project text/graphics using vector means, you need the feedback. You also need speed, and a fair amount of deflection. That means the device holding the mirror has to fast and lightweight, with little mass. The more mass it has, the more overshoot/undershoot becomes an issue (resulting in poor repeatability, and "ringing" on corners or other sharp position transitions).
What you ultimately want to look into is what is called a "laser galvanometer"; these devices work real similar to an analog meter movement - except they have a form of position feedback. They are very fast, and very lightweight (well, the moving parts are). Position feedback is generally done via capacitive sensing, or optical reflection.
People have built homemade galvos, but it isn't simple; from what I've gathered, it can be a very painstaking and frustrating process - but the reward can be worth it in the end.
Again, attempting to do this with speaker drivers or other methods without feedback will yield little more than a curiosity (not to say that such a device can't generate interesting, fun, and beautiful patterns; it most certainly can!); if you want to go beyond that level, you need the feedback capability (if you can in some way incorporate such a method in a speaker driver mechanism, you'll be halfway there - unfortunately, such linear drivers of that nature tend to have waaaay more mass than you want for such use).