Can I power a DC fan from li ion to nimh?
In raw capacity, rechargeable NiMh AA Energizer had 30 percent more energy storage per dollar than the Panasonic Eneloop AAs, so your devices should run a little longer between recharges.
 Your costs may vary.  ($20/8pc) or $7.50 per 3AA's   

Some users test results Energizers had an average of 1,888 milliamp hours (mAh) or 2.3 watt hours (Wh) of discharged capacity. 

So 3 AA's is 6.9Wh so ~1.3W @ 3.5V will yield 5.3h more or less.  with 1000 charge cycles at rated capacity current.    

Note they advertise 2000mAh at a lower current for 10h.

Thus the cost to compare is $7.50/6.9Wh = $1.08/Wh

Then compare cheap Skywolfeye 5 X 5800mAh Li-ion 18650 3.7V $10
which are probably only 1200mAh not 5800 (fake) are expected to be ...
$10/5x5.8Ahx3.7V= $0.09/W but probably $10/5x1.2Ahx3.5V = $0.38/W and some may last a few cycles while others 250 cycles. you YGWYPF ($) buyer beware!