Unfortunately, if the message was already read or you're past the point when it can be edited, then you're out of luck. The message can't be deleted. You're not done yet though, depending on just what the mistake was.
If you merely sent someone an inappropriate or insulting text (that they weren't supposed to see), then you can always be a little clever. Depending on your relationship with the person, you can probably just use a simple excuse, which may even be the truth. Just state that you sent the message to the wrong person, and that it would all make sense in context. This is probably the least painful method, if it will work.
If you sent something much worse, then you can always move on to lies. Thankfully, it's considered a fun prank now to jump onto someone's online accounts and change their information. If you say that your roommate/brother/sister/friend/enemy sent the message while you weren't watching, then it should work too. Everyone knows someone that would actually do it, so it's not a bad excuse. Hackers are also a current bogeyman, so you may be able to blame them for embarrassing messages, if the other person isn't too tech literate.
If worse comes to worse, you can always just hide your shame and block the contact. Deleting a contact on Skype isn't all that hard. You just need to right-click their name and choose to remove them from your list. If you wish, you can also go a step further and block them.