just one thing,when using a battery without a regulator,what's the worse that could happen?
The worst that could happen is a too high voltage, but if you make sure it ain't too high from a fresh battery, you're OK.
You call it a fluctuating voltage, but that would mean that it went both up and down and since a battery voltage only goes down, it would be better to call it a descending voltage (or something like that).
If the current draw is low, you could use a zener diode and a resistor to regulate down without a dropout voltage worth mentioning.
Square 9V batteries (PP3/"transistor batteries") have around 100..150mAh (some 9V batteries are built from 6 AAAA (4xA) cells). Alkaline AA-size cells are more than 2000mAh.
So, 9V x 150mAh = 1.35Wh
and 1.5V*2Ah = 3Wh
The AA, which costs around a fourth of a 9V battery has got more than double the power available and with 6 cells you get 9V @ 18Wh.
A 4 cell NiMH will be up to 5.8V right out of the charger and is flat at somewhere between 3.6V and 4.4V (depending on current draw [4.4V at a low current draw] and specifications).
So, it starts at a voltage that could harm a controller and only have part of it's discharge time in a useable range.
Much better to use 6 cells (5.4/6.6V flat and up to 8.7V newly charged) to make sure it will always be higher than needed and then use either a zener regulator or an LDO regulator.
The ultimate best regulator for a battery supply is a SEPIC switcher, as it allows the battery voltage to be higher or
lower than the output.