I love it when this happens.
I used the info in my original post, stopped by Radio Shack on the way home, purchased a 3V Lithium battery the same diameter as my V 625 U battery. Two companies at least make a replacement for the 625, including Kodak and Ray-O-Vac. Don't know the other manufacturers, but RS had one tonight that the sales clerk last night couldn't find. Oh well. I also bought a 3000 NCD (?) LED bulb. It is a 5mm bulb. The battery is thinner than the original, but works OK. The way I did it was to put a piece of double sided tape on the battery negative side (fits against the roundel) and the reassembled. The battery doesn't fit inside the roundel, thus the double sided tape to hold it in place. And, since no electrical contact takes place on that side of the battery, no real problem having the tape there. The Radio shack part numbers are: 2300164 - Lithium Cr1620 battery, and 2760307 5mm Red LED 3000 MCD. I removed the incandescent lamp, fitted the LED in its place, soldered the leads in place and then tested it. Worked perfectly. I reassembled it and viola! Now, the best part of this is, since it is a Red light, it won't destroy your night vision when you need to use it. An added bonus.
I don't really know how long this battery LED combo is supposed to last, but from what I've heard, it might outlast me.
Just remember. Short lead from the LED connects to the metal piece under the spring and the long lead to the metal part that touches the bulb.