Battery power supply - power regulator

I am trying to run the arduino with 4aa NiMh batteries.

The reason I use 4 batteries is because I need a lot of power for Leds. Therefore I did connect the leds directly to the batteries (which works)
For the arduino I plan to use some kind of power regulators like the Anyvolt micro.

Would that work?

Also I am trying to find a protection module which stops the batteries to overdischarge. But the only modules I find are for LiPo batteries.

Is there any module to protect the batteries? It should be very small in size because it needs to fit inside a tube with 2.6cm diameter.

Any help is highly preciated. Thanks,
Jens