The THC3 red from LSDiodes.com seems to work pretty well on a board intended for a white 5mm LED. I've never done one in a Dorcy, but I did one in a first Gen Inova X1 and ran it through several charge cycles with an NiMH cell. I think the specs of the red THC3 are something like 2.2 or 2.4V at 100mA so a circuit that sends 20-40mA at 3.6-3.8V seemed to work pretty well.
I've killed an AWFUL lot of red LEDs messing with various direct drive setups. Coin cells have so much internal resistance that they aren't likely to kill the LED very quickly, but you'll get a lot more runtime out of the 2032s vs two 2016s, of course at less brightness.