You could clip it directly on his tie. Also tape the tie down with gaff tape. Another option, hide the mic in the knot of his tie. Just because he is a CEO, does not mean you should feel intimated to talk to him. Inform him of the problem you are having with his tie brushing the lav. Most CEOS ( and I’ve hung or hid mics on a lot of top end auto execs here in Detroit) like to know if they sound or look good or bad. They are very image conscious. He is trusting you to make him sound good. Sometimes the hardest thing in dealing with CEOs is the junior executive ass kissers that are applying the pressure on the crew for no reason other than they think it makes them look in charge.
Boom mic is good option, but not for a talk show, unless you have dedicated boom op(s).
edward chick