There are no 4Ah 18650 batteries, so whoever is selling that is lying to you. The highest capacity 18650 battery that I've seen is a 3.4Ah battery, and there might be some 3.6 Ah batteries, but those are special bulk order. These batteries are usually $15-20 each depending on who sells it and if they have protection or not. Personally, I've been getting rid of my cheap 18650 batteries and bought some better ones now (Keeppower). AW, Eagletac, Pila, and some more are also good brands to look out for, check the electronics and batteries section for more.
The 17670 is a smaller Li-ion battery then the 18650, so it will give less runtime and probably similar output.
As for output, I'm not sure if 1x Li-ion battery is enough, or if 2x CR123s gives you more output.
As for runtime, it is easy to calculate. Assuming we have a 2.4 Ah 18650 battery, the battery's capacity is:
3.7V X 2.4 Ah = 8.88 Wh.
The LED is consuming:
3V X 1 A = 3 W (3V @ 1A from Cree's data sheet)
Assuming the driver is 85% efficient
3W / 0.85 = 3.53 W total power to both the LED and driver
Now we get to runtime:
8.88 Wh battery / 3.53 W draw = 2.5 hours runtime.
2x CR123 = 2 * (3V * 1.5 Ah) = 9 Wh
Actual runtime will differ depending on driver efficiency and voltage characteristics, as well as the battery's characteristics.