How to calculate 18650 battery use time?
Assuming that the "a normal power bank" uses the very same 18650 battery with same 2300 mAh capacity, the problem has the following solution:

Step 1: determine the mini-fan power rating. The normal 18650 battery (3.7 V 2300 mAh) has total rated capacity of 3.7 * 2.3 = 8.5 W-hours. The powerbank must have a DC-DC converter to 5 V output. Assuming efficiency of the converter as 80%, the effective capacity of the "a power bank" is about 7 Wh. Since the mini-fan can run for about 7 hours, we can conclude that the fan rated power is 1 W. This is at 5 V power supply.

Now, if you use TWO 18650 cells of the same kind as in "a normal power bank", and design another power bank with 5-V output and assuming the same DC-DC efficiency, the mini-fan will last TWICE AS LONG, by simple arithmetic.

Step 2. But if you plan to feed the mini-fan  with 7.4V (two batteries) directly, the following calculations may apply. Without DC-DC conversion, the capacity of two-cell battery will be about 17 W-hours. However, the mini-fan motor will be running at 7.4 V instead of 5 V, so it might be consuming (7.4/5)^2 = 2.2 times more, or about 2.2 W. So the runtime will be about 17/2.2 = 7.7 hours, only 10% longer than the original setup from "a normal power bank". It might, however, move more air over that time.