The laser uses current to glow, not the battery. The laser will burn out if its current is too high, not the battery.
The battery is NOT rated for 105mA. That is current. The battery is rated for 105mAh, which is how long it can supply 1mA (105 hours) or less.
The power supply circuit is able to supply from no current to 1.5A, or up to 0.7 times the current rating of the transformer. The load takes as much current as it needs.
You must measure the current in the original laser circuit for you to be able to calculate the current-limiting resistor.