When I did build a solution maybe 10 years ago, I think I used silicone-based glue to glue the tiny mirrors onto the rim of the loudspeaker cones. The loudspeaker cone was mounted with rubber and a hard type that allowed me to remove much of the cone without getting stiffnes problems. But I have seen references where the mirror has been driven by the center of the cone too (should allow a smaller/cheaper speaker than I used), like in this link:
http://spt06.chez-alice.fr/00/scan1.htm

Richard: Remember that a x-y scanner with a reasonably number of scan lines either has to be very small, or has a very high-intensity laser because of the big length of the total sweep. And with a high-intensity laser, you will have two important problems:
1) there must be no reflective surface in the target zone, that can allow the light to reflect into the eyes of a viewer.
2) you must have a very good hardware watchdog system that will cut the laser output in case the modulation stops, or you may get a fire.

Using a rotating multi-facetted mirror combined with a linear deflector is the best way for building a x-y scanner, but you will get a stronger display by instead using separate X and Y modulation and vector-plot any information. The disadvantage would be that vector-plotted information changes in intensity with the complexity of the design, unless the LED instensity is adjusted to the drawing time.

When I originally built a solution, I had a very weak laser. I think I ended up with a laser diode from a CD reader (could have been from a low-speed CD writer). I have been thinking about building a new display using the much stronger laser diode from a high-speed DVD writer. But the dangers involved must not be ignored. I have been looking into using two secondary light sources with photo diodes controlling a hardware watchdog to make sure that if one of the mirrors stops moving, the laser gets instantly deactivated with no involvement of any processor.