Hi Wonderboy,
I was wondering what components you would be happy to use,
your earlier diagram includes a potentiometer and a diode,
and what might be a milli-ammeter.
I'm not sure which component is the LDR, i guess it might
be R2 which is shown as 16K-ohms.
Your approach of having some current going through the relay
coil, bringing it nearer to the point of operating, is well
known as 'biassing' and is used with many devices.
However the arrangement you have shown in your accompanying
circuit does not look very likely to work.
In fact the impedance of the LDR you have chosen is far too
high to be used to operate a low voltage relay directly.
Best match i found with a quick search was 'VT 53N1' which
is quoted as 500mW 16k/1M.
This may or may not be the one you have.
If you can find a much lower impedance light sensor,
you might be able to work a reed-relay.
Although as 'Crutschow' points out this is a long shot.
However, with two or more LDRs in parallel, you might be
able to operate a reed relay.
This will of course be backwards, that is if it works, then
it would operate when the light is shining.
Which is not the way round that you want.
Thats not so bad, it could drive a relay to do what you want.
There used to be reed relays with an extra contact for 'N/C'
but i havent seen one for a long time, they may not be around
any more.
Briefly, with three or four in parallel you might be able to
operate a reed relay. But you would have to choose a sensitive
one. And maybe bias it.
Otherwise, its down to a different arrangement altogether.
(unless anyone else has any ideas?)
Best of luck with it,
John : )