What did you think the handle of the Master Sword was made of? Anything other than metal would be too fragile to handle all of the bashing, slashing, chopping, and other impacts that Link puts it through, all magic aside. It does look like a stone of some sort, though, doesn't it?
Anywho, yes, you can make metal blue, but it's a complicated process that's costly and can also weaken the metal to a certain degree, as I understand it. Painting it would look ugly and/or require constant touch-ups.