Okay, I'm not sure where to post this question, so I'm putting it here since I read this forum the most.

Is it possible to put 10AA 1.2V NiMH batteries in series (in an inexpensive $2 holder) and power an LED camera light that way? My plan is to replace the typical 35 or 50 watt light bulbs of an on-camera light with a 3-watt LED bulb. 10AA rechargeable batteries with a 2500mAh rating should power that for 10 hours (2.5Ahr x 12V / 3W = 10hr).

I need to figure out how to wire an XLR power cable (or cigarette adapter) to the PP3 tab connectors of the battery holder. If anyone can shed any light on how to do this, or provide a diagram, that would be much appreciated!

Hopefully, the result is an inexpensive 12V DC source that is much more compact than a typical battery belt.

you can do that, but there are several things to check.
First, LEDs do not use 12V but 3.5V or a multiple of it, so you need to check
if the light you will use really require 12V.
Then, small ni-mh cell are not made to deliver high current (usually equal or less that 1 load. so if your cell is rated 2500mAh, you should not ask more than 2.5 amps.
And finally, you would get a better price/power/size/weight ratio by purchasing li-ion cell (usually 3.6V 2000mAh).
see www.batteryspace.com, they got a huge offer of cell and charger, as well as shrink tube, holder etc...
For info, a 3W led is almost nothing compared to a 35 or 50W lamp
and the aperture of such lamp is very small, so you get a very undesirable hot spot in the middle of the picture while the border will be dark.
a diffuser will be helpfull , but a lot of light is lost in the process.
i built such a led lamp with 8 X 1W led, in a 16/9 layout and i am very happy with. but for subject more than 9 feet far from the lamp, it is useless.