I took Anastasia's advice, and vacuumed the dog this morning.
Much to my surprise, he merely looked at me as though I had taken leave of my senses and let me get on with it. It did not seem to bother him at all.
I hope to get DH to take a photograph of this process in the next few days :-)
I will also take the dog in the back garden and give him a good brushing near where the bird feeder is, so the birds can help themselves to his shed fur for their nest-building, which they are already starting .........