Ah, hang on
I was wrong, but not on the crucial point.

My examples aren't possessive adjectives at all, they're nouns with an enclitic suffixed to show possession.

The possessive adjectives (or possessive determiners) in English are:

My
Your
His
Her
Its
Our
Their
Whose

...and the corresponding possessive pronouns are:

Mine
Yours
His
Hers
Its
Ours
Theirs
Whose

"One's" is just a noun (one) with an enclitic ('s).
(Vice Admiral Sir Charles Cockbrush KCB MBE DSO, who is finding it increasingly difficult to log into b3ta.com wants to duck your aunt and kick your puppy, Tue 12 Oct 2010, 11:47, 1 reply)

This is why I'm confused.
Why the clitic? I don't understand why one can't just write 'ones hands'. It doesn't make sense.
( The Awful Puppy Bakery is still bored, Tue 12 Oct 2010, 11:50, closed)

Same reason you can't write "womens hands"
"One" isn't a personal pronoun, it's just a common or garden noun.
(Vice Admiral Sir Charles Cockbrush KCB MBE DSO, who is finding it increasingly difficult to log into b3ta.com wants to duck your aunt and kick your puppy, Tue 12 Oct 2010, 12:09, closed)

I see your point.
I'm glad we cleared that up. Every day's a school day.
( The Awful Puppy Bakery is still bored, Tue 12 Oct 2010, 12:16, closed)

Hmmmm

(Speshal, Wed 13 Oct 2010, 0:41, closed)