Thanks MikeMl and Hero999!
Hero999, I am modifying this working device and all I can see is what I have described. The batteries are standard 1.5Vdc AA. so I do not know if they have the resistance that you mention. I can say that the LED will only be lit for a couple of minutes at most at any given time. Don't know if that matters.
MikeMl, so I was on the right track, if I get a 12Vdc power supply and as close to 445Ω resistor my original circuit should be OK. What affect will the coil of a 12Vdc relay have on this circuit? I know there is inductive reactance in the coil. I assume that I would need to find that value and subtract it from the resistor's value to keep the circuit "balanced" so to speak, correct?