Most colleges have a period of time, usually the first two weeks, where students can drop without a W appearing on the transcript. There is a period of time, sometimes the two weeks but usually less, where a student can add a class without instructor permission, too. I am not familiar with Yale and how the “shopping period” compares to that but that’s the baseline at most universities.
*Some universities have the drop before W later into the semester but you usually cannot add after the first week or two.