QED: While I know you are looking for a mod, there is an easy off-the-shelf solution: here in the Canadian North West where winter nights last 19 hours long, a lot of people use 2xAAA bike winkie lights, red, which have a pocket clip, clipped to their dog's collar. These are definitely bright enough, and at $3.50CND not expensive. They are about the size of a 9V battery, but much lighter. They run for about 100 hours on 2xAAA Nimh cells, even in -30C weather. Putting a small rubber band, such as a strip cut out of a bike innertube around the open end of the clip, makes it tougher for the dog to lose the light. These lights are available from the Mountain Equipment Co-op at MEC.ca.
While I am not an LED expert, it seems to me that the bike community has had LED lights before any other group of outdoor users, (back to about 1985 or so, so they seem to be the cheapest, mass-production stuff around, with rubber-'O' rings and long run times!
We will still have midnight sun or twilight here until about 0100 now, sunrise again around 0530, so the darkness is coming back after a summer of midnight sun!
Enjoy your walks!
