He just let the hair fall in dry. It would have been easy to collect and toss so long as he didn't turn the faucet on.
I will say this: this episode proved Shane doesn't know much about head shaving. His only poor moment of the episode.
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Yoblazer: http://i44.tinypic.com/5nw45i.jpg
Watch and you'll see... someday I'll be... part of your world!