I'm level 5 and I've tried wolf, bear, panther, badger. Tried reverting the override folder back to its original state, tried another save, tried DebugMode with other saves to level me up to Wildshape and test it; absolutely nothing works. I would have thought this game might have had most of its bugs ironed out a decade after its release, but I guess not!
Now that you describe it that way, this is familiar to me. I think there was a 1.69 bug where a shifted toon is assigned some command (like equip the skin item) by the horse scripts and that would lock up the PC's input queue somehow and make it so that the toon could not attack. I don't recall if The Krit fixed this or posted a workaround for it. I will do a little searching and see what I can find.