CR2032 is generally not suitable for driving lasers. For maybe a momentary 20mA (that's 0.02A) drain, maybe.
CR123A *should* work alright, but it depends on how efficient the driver is. The IR diode needs something like 2.5 volts. A driver requires a bit of voltage for itself, so if the driver's voltage plus the diode's voltage is more than the battery's voltage, the laser may dim or cease lasing.
What 3V primary (non-rechargable) are you using?
Amperage on a multimeter is generally not a good thing to test batteries with. The idea of an ammeter is to measure the amps flowing through a circuit while modifying that circuit as little as possible. Therefore, the ammeter is basically a very low resistance wire, and testing a battery with an ammeter simply shorts the battery.
On a protected lithium ion cell, this is usually enough to trip the protection circuit. Recharging the battery on many chargers should reset the protection circuit.
I would suggest buying and waiting for the appropriate battery.
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Chargers have that disclaimer because with the larger cells like 18650, 22650, etc., you can charge them with a higher charging current that would otherwise damage or destroy smaller cells.
I wouldn't recommend charging that 14500 in that 18650 charger. If you have more Li-Ion to charge than just that one 14500, you might consider investing in a nicer charger that can charge at high and low currents and fit small and large cells.
i just wasnt sure if the value is important or so.. ._.
