I have done this for a guitar - I had a Tele with a really nice neck but way too heavy. I took the plunge and made a body myself from scratch, chambered mahogany with an Ash top, the second attempt turned out well : )
It may actually turn out to be quicker and easier to make a new body (or have one made) than to modify an existing one. If it turns out too light, you could always add some weight in the cavity.