A couple comments from my attempt to ID a very similar tree that had me confused might be particularly of interest to you. The first comment is me quoting a retired dendrology professor that helped me out:
From the pictures you provide, I favor Carya ovalis, false shagbark hickory, for the identity of your mystery tree, based upon the bark, bud and fruit. I concur with you; the fruit husk is too thin and the buds too small for shagbark hickory.
In my opinion, pignut and false shagbark hickory are very closely related, and possibly not worthy of recognition as separate species, an opinion I share with others. I do not agree with your reference. Pignut typically has 5 leaflets, and false shagbark has both 5 and 7 leaflets with the majority of leaves having 5 leaflets. Major clues for me were the nearly spherical shape of the fruit, the thin husk and the narrow and short shags of the bark, not the long (2-3 ft) and wide (4-6 ins) shags of mature shagbark. Also recall that shagbark leaves are very large, 16-24 inches long.
This may be carya ovalis ? Or a hybrid of it “x” C.glabra
"Several vars.recognizied, some of these perhaps better considered as mere forms "
I spent the day today thinning around hickorys here, many of which I have no idea what kind they are…?