Cats' whiskers have nothing to do with their balance. The whiskers are there so that a cat can assess if they can fit into a certain space for safety. A cat's whiskers are as long as their bodies. When a cat reaches a tight space that they try to get in and their whiskers touch the sides of the openening, they will not enter that space as the whiskers let them know the opening is not big enough. Your kitten's unsteadiness has nothing to do with the whiskers. It maybe because he's just young. You should take him to the vet to put your mind as ease.
By the way, cats inner ear is used for their balance. Did you look inside his ears to make sure they are clean and no infection? That may be your problem.