It's also possible the edge is more polished than is best for it, depending on what compound you used for stropping it. With the stainless used in most kitchen cutlery, they usually work best when they still have some toothy bite for slicing - the same sort of bite you'd definitely feel in your fingertips. If polished too far, they'll lose aggression for slicing tasks, but can still rely on the thinness of the edge geometry for simple cutting tasks like in paper, or in cutting most fruits & vegetables, which doesn't require a very keen apex to do (except for tomatos, which won't slice easily with a rounded/blunt apex). A lot of factory edges on kitchen knives rely on that specifically, as they can still work fairly well for what they were designed to do, but also won't be sharp enough to risk much injury to the fingertips in kitchen use. I used to notice the same tendency when feeling the edge with my fingertips, if I polished them too much. It tends to round over the apex somewhat, if not done very carefully over a hard stropping substrate.
An edge that's thin, highly polished and acutely keen at the apex will definitely cut the skin if not careful. The difference will be in whether the cut is felt or not, as the high-polished edge can cut you so cleanly, you might not even feel it. So, if the edge isn't cutting your skin at all, but doing other things well enough, it's likely somewhat overpolished or slightly rounded at the apex.
If it were me in the same circumstance, I'd just sharpen on the 1200 diamond and do as much deburring on the hone as possible, and skip stropping with the compound. Then test the edge to see how it cuts in the kitchen tasks you normally give it. Whether it shaves or not isn't necessarily important for any cutting task except shaving.