Cockney wh-dropping

Solution 1:

The spelling (and for that matter also the etymology) is essentially irrelevant in the pronunciation of those words, and other WH- words with initial /h/. Sound changes apply to sounds, not spellings.

Hence, any lect that drops initial /h/ will drop it on these words, too. I can't tell you anything about Cockney lects in particular, but linguists have known for over a century that sound change acts with blind necessity, as the Neogrammarians put it.

Solution 2:

I suspect that who- words are pronounced with varying degrees of aspiration in all accents and that there is no consistency. Certainly, Oo you talkin’ to? or Ooz ‘ouse is that? would not be unusual in many parts of Britain.