The OP seems to be confusing the grappled condition with pinned. Grappled does not cause you to lose the ability to attack with any appendage you may normally attack with, regardless of whether or not that appendage appears to have a hand-like thing on the end of it, was previously a hand that grew claws, or is an actual hand that is made into a fist, wears a spiked gauntlet, or holds a weapon.
The attack it prevents you from making is a 2-handed weapon attack, which has 1.5x STR mod bonus to damage. The rest of the effect is a penalty to DEX, a penalty on attack rolls that aren't grapple maneuvers, and the inability to move or make AoOs. Most grapple-based monsters will never take the -20 to avoid having the grappled condition when grappling, because these other penalties aren't that bad for them and they are generally focused on killing things rather than restraining them.
Another thing that leads to confusion has nothing to do with whether or not appendages are hands or hand-like - it is in the applicable definition of "action" for the actions to which the grapple restriction applies. The OP is interpreting a full-attack action as the action type / level to which this should be applied, and is trying to make a reasonable judgment on how to extend the rule there for combatants that don't have a single weapon or attack form.
If you follow that logic, no creature that has hands and uses them with other attack forms can make a full attack action when grappled, e.g. a creature with a claw/claw/bite sequence would get none of those attacks because the whole sequence is an action that requires both hands to execute. They could only make a standard action attack, 1 claw OR 1 bite but not both.
If you reduce it down to the individual attack action type / level, then neither claw attack is an action that requires 2 hands, and thus both are allowed.
The intent is to deny the use of a move action to move, and to penalize the use of standard actions or full attack actions if the grappled creature chooses not to grapple. There is no "almost full attack" action. You either take a full attack (with all penalties and every attack form desired) or you take a standard plus anything you might want to do with a move action that isn't moving. And attacks with 2-handed weapons are not allowed in either case.
The originally suggested ruling imposes an additional penalty on creatures that use multiple attack forms and desire to make a full attack, and that ruling is not consistent with RAW. Allowing full attack for a humanoid who wields a single weapon but not for a character or creature build that uses multiple attack forms is unfair to those other builds. You might just as easily say the former has his sword arm grappled and is denied his iterative attacks because switching his weapon to his other hand is an action that requires 2 hands to execute. Grapple affects the body, not specific limbs.