One more question: Detect magic does not tell you immediately that I it is a shapechange trait, it tells you that there is a bit of Transmutation magic going on. Would you allow an Arcana check to determine that it is a shapechange trait?
I'm actually of a much more literal interpretation of spell texts, so at my table [spell]detect magic[/quote] wouldn't tell a character a school of transmutation for the change shape ability since "polymorphs" not being italicized means it isn't actually the spell being cast, and only spells have schools of magic.
However, that is itself a clue at what kind of magic has been detected, since something without a school to it is likely an innate trait of a creature (and at least clues the player in to not trying to use [spell]dispel magic[/quote] because that obviously won't work, given that an effect without a school of magic also doesn't have a spell level assigned to it, and whether a dispel is successful or not is entirely tied to relative spell levels).
As for an Arcana check, and what it would reveal for the player. I'm of the mind that a DM should not tell players what their character's believe, so I don't use ability checks as a means for a character to reach a conclusion, but as a means to gather evidence. In this case, though, the end result is likely not to be all that different between the two approaches - where a DM might answer a successful check with "This magic is a change shape trait", I would answer the check with "the magic appears to manifest some alteration of the physical form" and the player is likely to realize that bit combined with the earlier evidence (magic detected, no school to it) supports their belief that it is a change shape trait.