Well, the only real benifit of Li-ion batteries is that you can recharge them, and they take up less space. Since this build doesn't have sound you should be fine using 2 AAs per amber LED.
Yes, you will need a different resistor with the AA batteries. Here is a good calculator: http://ledcalc.com/ Set the input voltage to 3 volts, and the LED voltage to 2 volts, with 1000ma of current.
I calculated that you will need a 1.2 Ohm, 2 watt resistor for each LED.
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