After you delete it, you are going to have to renumber your other icons - unless it was the last in the list. Then, you need to go to your control panel and correct the names, and submit the settings. You should be good to go then.
However, I don't recommend it because then your other posts will get messed up because the icon is numerically named. Personally, I would overwrite the icon you wish to delete with another one. That way, there won't be an icon shift.
Amy