A lot of PWS is rocky, as in solid granite, and the shallower anchorages are sometimes debris slides or river drainages between the shore and the drop-off. If you go aground the highest probability is that you will hit a solid outcropping, there is very little soft in the Sound.
All you have to see is the steepness of the islands and you know it drops off fast, depths in excess of 3000' some places. Shallow anchorages with flat bottoms and good holding ground and protection are available, but not frequent. Those of us who frequent the Sound develop a catalog of preferred anchorages, but don't often share them because they tend to be quite small and only hold a few vessels before becoming crowded.
If you only have 200' of chain those anchorages are even further apart. Plan to anchor in 50'-150' of water.