Yes. This is hard. I think the best single thing to keep in mind is that quiet kids have long "runways." That is, the noise is surely a challenge, but quiet kids can accommodate over time, it just may take quite a while. The biggest thing in my opinion would be not to push the child to speak up in class beyond the whisper. If it's a whisper for now then it's a whisper. It's better than complete silence and probably bespeaks a capacity to speak up more loudly eventually, when he or she is more comfortable. It might be good to talk to the teacher about that too; to advocate patience and gentleness versus any kind of push, which often backfires with these kids. He'll speak up when he's ready and that might be a while - requiring patience from you and the teacher, but it will happen eventually.
Another thing to keep in mind is that just because quieter kids don't speak up doesn't necessarily mean they are not engaged, entertained, happy and learning at school. Often they are, they just don't want to speak up. So this whisper doesn't NECESSARILY mean that this school is actually problematic at all, that the kid is unhappy - as long as you can manage the teacher's reaction (maybe give the teacher a copy of Quiet!). The hard part of all this is that the school, the noise, the overstimulation might be a real problem and the child might be unhappy there and then you will have to think through your alternative options. You have to really observe that closely. My point is that the whisper at public speaking moments doesn't always or necessarily mean there's a big problem in general happiness at that school, and that the kid is just plain in the wrong environment. He may overcome it and any other small challenges eventually with gentle patience, and ultimately thrive there.
Finally, he may indeed be more comfortable in a school with smaller classes and more individualized learning; easier said then done of course, and often quite expensive sadly, but smaller classes can help these kids get more confident more quickly.
Any other readers have any thoughts? this goes right to the heart of the challenge of raising quieter kids today.