I used to fish this area a lot, especially the flats near Watts Island, which is where some of the best flounder and weakfish action took place for many, many years.
First and foremost, if you don't have a screen enclosure to ward off the flies and mosquitoes you will be eaten alive this time of year. Early spring is when the marsh comes alive with all kinds of hatching, flying, biting critters.
Yes, you can anchor in Cod Harbor, as long as the prevailing wind is from the southwest, north or west. An east wind will beat you up real bad. It's a pretty long fetch across Tangier and Pocomoke sounds and those waves can really build.
If I were taking refuge from a storm there, and looking for a completely sheltered anchorage, the best location would be near Janes Island State Park, which most of the time, even during a hard blow, is pretty well protected in all directions.
As for anchoring near Smith Island, I really don't know of a single location where you would not be in a channel used by local watermen. There used to be a small pocket of deep water near Boat Island, but that silted in many years ago. Other than the Big Thorofare itself there is no deep water location large enough to anchor at Smith Island. However, you can tie up at Allen Tyler's restaurant pier while having lunch and later tour the island.