As it is written, I'd say you are good to go my friend. Bite of the Weretiger, as our example is written as (emphasis my own):
Your hands become claws, granting you two claw attacks, and your mouth becomes that of a tiger, giving you a bite attack. You can attack with both claws at your full base
attack bonus, but your bite attack takes a —2 penalty (as if you had
the Multiattack feat).
The spells specifically says you pode use the claw and bite attack, but it doesn't say you não pode use your claw/hand to wield your weapon instead. The spell also states:
If your base attack bonus is +6 or higher, you do not gain any additional attacks.
So, if your BAB is +6 or lower (unlikely as this is a level 5 Druid/6 Wizard spell), you would be granted an extra claw or bite attack. If the BAB is higher, you can attack with your normal amount of attacks, you just have more kinds of attacks to choose from.
This DM would rule that an appendage needs to choose if it will go natural or weapon attack, then if an appendage has already made its attacks (claw holding a sword), it is done for the round (it's been busy attacking with the sword). The other appendages, including the new bite attack can still be used though.
As for the spell affecting the somatic component for spellcasting, the spell doesn't say that it interferes, so I wouldn't assume it does, it is a high level spell after all. If your druid had the feat Feitiço Natural, this DM would be even more inclined to approve it.