Basically anything in the area where the quiet pool is, including end rooms , has probably the lowest noise issues at the resort. Thus, you could request the quiet pool area in general, but make sure to also ask for higher floor (the higher the floor the less the risk of noise, which is true throughout the resort). I have been in the lock-off 2BR next to 4136 and noise level was low, although there was sometimes hallway/stairway noise as the stairway is right by 4136. Thus you could request that very end dedicated studio but the noise level is not going to be quieter than many other places in the quiet pool area. However, it does give you easy access to the stairway to ground level to go to the quiet pool and to have shortest walk from BWV to Studios. Note, I do not think there is a 5136, 4th floor is the highest there. Go here to see room numbers and locations:
https://www.disboards.com/threads/bwv-room-view-and-number-maps.3794835/
I am not sure what you mean by wanting a quiet area but not being bothered by the Village Green. Does that mean you would accept Village Green area? The studios in the Village Green area are all preferred view, and give partial boardwalk view, but noise levels would be higher than rooms around the quiet pool. Also, if you request Village Green area, make sure you also request higher floor. There are studios on the second floor right above the Wyland Galleries that essentially have no view at all because the arches of the Galleries extend up to that level and block views from the rooms.
There are also rooms in an area called the Activity Lawn. which rooms are across the hallway from the last half of the boardwalk view rooms. The rooms in that area have views of the waterway. Back when BWV was created, there was actually quite a bit of activity on the Activity Lawn area, such as croquet events. That has been gone for two decades, and though it is still called the Activity Lawn area, there is no activity whatsoever on the large lawn area in front of the rooms. Those rooms remain quiet except for boat horns, as it is an area where the boats usually set off their horns when passing, since it is the area near where the channel mets the bay.