The laser module may indeed be utilizing the built=in internal resistance value of the LR44 batteries to keep the laser from drawing excessive current and burning up. What I would do would be to try and power the laser using 3 LR44 batteries in series and measure the current consumption that the laser draws. Then if you power the module with a fixed external regulated 4.5vdc power source, just add a series resistor that results in the laser drawing the same amount of current as it was while being powered by the batteries.
Lefty