Creio que squeaky quer dizer oleoso, gorduroso. Em Português de Portugal, eu traduziria como cabelo oleoso

cabelo super-limpo

squeaky clean = completamente limpo, totalmente limpo, limpíssimo.

--------------------------------------------------
Note added at 4 hrs (2010-12-27 23:16:30 GMT)
--------------------------------------------------

Here's a hair that has just been washed, either by having been immersed in water when swimming, or by showering with a detergent shampoo.
The dirt is gone, and so is the oil. All that's left is a smooth strand of hair. If you run your fingers through clean hair like this, friction between your fingers and the hair itself will make the hair vibrate just as if you were running your finger down a violin string. That's the squeak
http://www.worsleyschool.net/science/files/amusement/hair.ht...

Did you ever notice that when your hair is wet, especially after you've just washed it, you can run your fingers through it and it squeaks?
That's where the expression 'squeaky clean' comes from!
The question is, why does your hair squeak when it's clean!
Let's look at some hairs close up and find out ...

squeaks - chia
squeaky clean - tão limpo que chia
why does your hair squeak - por que o seu cabelo chia

Ao frotar a mão com o cabelo (couro cabeludo), se ouve um chiado. Como quando lavamos a mão com sabão, aquele chiadinho...

Minha opinião.