Bozon explained it pretty well for ya Melvin. Wavelenth does not have a big effect on beam divergence until you start to cross into and out of multiple mediums. (shooting your beam through air then glass then air then water, and so on) Think about the divergence like this - the laser is a water hose with one of those adjustable nozzles on the end, the water coming out is the wavelenth and the nozzle is the laser optics used to change the divergence, no matter how you adjust the nozzle and mess with the angle of the spray of water it is still just water coming out right? Same with a laser, you can diverge or focus the output with the correct optics all without changing the wavelenght.
The power source will surely be provided my the aircraft itself, so I guess my earlier statement about the power used for prolonged use would be a problem is a null issue. That said, most IR lasers that can fit into a package the size of a dvd player will not be "on" all the time due to heat issues and will most likely be pulsed lasers. The laser I built for those rangefinders was about the size of a snickers bar, but once you added the turning optics, power supply, and device output lens the whole thing was about the size of a portable dvd player, that was then put into a larger weapons system fielded on humvees.
Blinding the missle will be related to the power output of the laser vs the projected area of the output beam. For example you have two flashlights both putting out white light, one is a cheapo flashlight you got from wal-mart and the other is a search and rescue grade spotlight, they both are projecting a 5ft diameter circle on a wall which one will leave you seeing spots for a week if you stand in front of it?