I'm inclined to side with Billy on whether the Alphas use a spell to transform (it looks like a spell to Harry because he's a wizard). They're a bit bigger bruisier than regular wolves, so it might be worth saying they're blocked when in wolf form - if the wolf body is still considered natural, they might just have trouble changing forms unless invited (say each shift means changing takes an action longer).
For a Hexenwulf, I'd go with blovked in wolf form, and the ability to change into the wolf form suppressed.
For Loup-Garoux, blocked.
For Lycanthropes, suffering suppression to powers.
For wolfweres, werewolves in reverse.
I don't feel as if shapechangers would be bothered much, if at all by Thresholds, they just don't pack that much metaphysical muscle. Harry is essentially a human, but has a lot of metaphysical power to draw upon, part of which is left behind if he crosses a Threshold uninvited. However,
in Small Favor, he draws in as much magical power as he can hold within himself before he enters the gigantic circle the Denarians are about the throw up.
So, apparently wizards have some magic that is internal and loads that is external. Shapeshifters like the Alpha's have, in my mind, all their supernatural power internally, so they might feel something as they shift within a restricting Threshold, but I doubt it hampers them in any real (i.e. mechanical sense).
I would think that a Loup-Garou wouldn't even stop short of any Threshold, as always it is a singularly unique creature.
Same goes for Fae, a typical Troll would be less bothered by the Threshold, as he doesn't have too much power beyond his physical might to throw around, whereas Lea as a lot. Of course, they are more hampered by their ectoplasmic bodies before crossing a Threshold in the first place.
I thought there was also some amazement from Harry about the Frog Demon being able to hold itself together through the Threshold.
As for Black Court Elders, the literature seems to say that it absolutely stops BCVs cold, and I'm not sure I'd want to waive that for Elders.
The Frog Demon was also superpowered by the thunder storm and he had a lot of real muscle to pound Harry into mush, if he had supernatural abilities beyond his body, he wouldn't be able to use them as effectively, or at all.
You might wish to say that BCVs have their power cut off, normally they draw on the ambient energies to animate their bodies, but within a Threshold this is denied. In effect, they would draw upon their own magical powers to keep up and about. A newb BCV would then fall to pieces within mere minutes, whereas an elder might last days, as long as it doesn't start slinging about magically. They are a bit like a golem, an inanimate body with a spirit, which is blocked by the Threshold.
So, in short, I would say that you should judge a critter by the power it can draw upon from outside of him-/her-/itself and what it needs to stay animate.