Yes its possible to solo Skeletron.
But imagine trying to solo all 3 bosses at once with no potions :P
http://www.youtube.com/watch?v=6kINLOg7ol8&feature=player_embedded
Oh yeah and use an enchanted boomerang (found in a gold chest) its easier with skeletron. As long as you have alot of potions :3
Taking out his hands are first nature. Make sure you have atleast gold armor :P