I'm not a big fan of hearing the 'h' pronounced in "when", or "white". I always imagine a burst of hot air ejecting from the speakers mouth when they say these words.
but "when" without the h is "wen" = Pathology. a benign encysted tumor of the skin, especially on the scalp, containing sebaceous matter; a sebaceous cyst
"white" without the h is wite as Old English = a fine imposed by a king or lord on a subject who committed a serious crime. or a fee demanded for granting a special privilege.
or "wight" as a supernatural being, as a witch or sprite. any living being; a creature.
or Wight as in Isle of Wight.
In other words, keep the h where it belongs! ;-)
Pee-ure for pure, on the other hand - ick.