We have a Kong ball called a Giggle ball. It's made of the harder Kong rubber, so it's a big heavier, but the sound it makes is a lot less annoying than a squeak. The sound is made by flipping the ball over, not by squeezing it, so it's a little more durable. It's still possible to chew it apart, but my dog is a power chewer, and he's more interested in playing with it than chewing.
As for the whining, is it really high pitched and quick, more like a yip than a whine? Our dog did something similar in the car, and we thought he was anxious because he would also get carsick. BUT, then we figured out that it wasn't anxiety, it was just his way of expressing how excited he was to go somewhere (usually the park). So, is it possible that it's just excitement, not anxiety?