Oh, well. I'm not sure it can be done "just" with Blockhead. Can the latest version of Blockhead also switch out the actor "skeleton" per race? You will need to have your actor use the creature's skeleton as well as animations. And as far as I know Blockhead can only replace animations by now.
OBSE does have a function to switch out a player's or NPC's skeleton, but it will require some scripting to make it work, as it needs to be re-applied every time the game was launched again. I think to remember the playable creature mods were already using "that" solution though, or they used a plugin-based switch without a script. But that switch is only actor-based and not affecting whole races at once.
And yes, the last problem will be the appearance. Yes, Blockhead will want separated body parts, while creatures usually have at most the head alone. Nobody's saying you can't just split a creature mesh into the 4 (5 counting tail, the head's usually already separate like I said) body parts respectively though, and then it can work. Just nobody's done that so far.
The most commonly used approach to playable creatures is still the same old I sued for my creature dragon shape shift approach. Make a "mountable" version of the creature, spawn it, turn the player invisible and make him mount. Of course you're then maneuvering it around like riding (you "are" riding it after all), but it's the easiest way. Once you unmount, turn the player visible again and de-spawn the "mount".
But yes, with a bunch of work, script-controlled switching out of the skeleton (which also switches out the animations) and Blockhead-induced custom body parts, you should very well be able to create a playable creature race. Can't say I've ever gone about it that way though.