I moved my thriving Christmas Cactus a few weeks ago from kitchen surface to fairly sunny window ledge

Its probably just sulking because you moved it, technically this is called a "physiological disorder" but I prefer to think in human terms, and say its 'sulking' ;o))

Regards trimming; Why not trim a few pieces off to tidy the plant up and insert them round the edge of a pot filled with gritty compost.

In this way you might be lucky and get a few new plants, and if I am wrong and your plant is diseased in any way, these might be an inurance against complete loss!

See here;

http://www.thegardenersalmanac.co.uk/Data/Schlumbergera/Schlumbergera.htm

Looks to me as if it could be dry, as you can see the ribs sticking out, perhaps it dried being in the sun, try giving a deep dip in water for say 30 mins then drain.

Lots of Christmas cacti do grow like this. They are naturally epiphitic, ie grow on trees like orchids, in the leaf litter caught between branches and tend to hang down.(This is why they shouldn't be put in normal cactus compost) What I do with ones with this habit is just put the pot on something to lift it and let it dangle.
You are quite right to have let it dry out at this time of year to rest it. When you begin to water again the stems will plump up and the flower buds should quickly form - you can control when they flower to some extent by when you decide to end the "drought!" Once the buds form do not turn the plant round as this could make them fall off. After flowering you can give one general feed. Slack off the watering around August.

The plant has a naturally drooping habit so the branches may not stand up properly again. Stand the pot on something to raise it up. Maybe use a clay pot to stop it toppling over? Or how about one of the tall 'jardiniere' pots on a stand like the Victorians used?

Thanks for your replies.

Can I just add that it is not the fact that it is hanging low that was really bothering me, but that the leaves (?) were wilted and weak looking.
I have raised the pot at the moment, and removed and replanted a few bits, and it is perking up a bit.

Make sure that you don't go the other way and overwater it! The symptoms look the same. Check the compost or get to know the weight of the pot when wet and dry.