Yes, you can definitely walk from the Dolphin --- a 5-8 minute walk, depending on where you are. Follow the outside of the building along and you'll come to the health club and then B&C. Stormalong Bay will be on your right and the YC on your left.
It's got good sandwiches and ice cream, but is very small and can get quite crowded. Don't plan to go after Illuminations gets out --- it gets swamped with people returning from Epcot. We've been given a pager, so at least we didn't have to stand in a line.
There's also a sandwich and ice cream place in the basement of the Dolphin (Not Tubby's Buffeteria --- just can't think of the name) which has always been much less crowded. Food not as good, but acceptable and less hectic, so keep it in mind as a back up plan.