Reading through natural spell it says "You can complete the verbal and somatic components of spells while in a wild shape." which seems to imply that the only reason you can't cast spells while wild shaped normally is that you're normally unable to fulfill the verbal and somatic components. If you have both metamagic feats are you able to cast a silent/stilled spell while wildshaped without natural spell?
Yes, you can.
Wild Shape works like the alternate form special ability which reads
The creature retains any spellcasting ability it had in its original form, although it must be able to speak intelligibly to cast spells with verbal components and it must have humanlike hands to cast spells with somatic components.
Since a spell modified by the metamagic feats Silent Spell and Still Spell does not have any verbal or somatic components, it’s no problem to cast such a spell while in Wild Shape (although any druid with the Wild Shape ablity should definitely and under any circumstances take the feat Natural Spell...)
Note that the Natural Spell feat also lets you "use any material components or focuses you possess, even if such items are melded within your current form". Without this feat "any gear worn or carried by the druid melds into the new form and becomes nonfunctional". So while you can use Silent Spell and Still Spell as a "substitute" for Natural Spell – you would still have a problem to provide the material components - if any.