I like it. Balthazar is the most natural spelling to me. I think it's a bit over the top, but I wouldn't call it unusable. There's Balthazar Getty at least, many people would be familiar with the name because of him. If not, you know, because of the Magi. ;)
Balt is the only nickname for it I know of. I kinda like it. It does need a nickname, I think.