It depends on what the bloodhulk originally was
You're correct that the bloodhulk is not implemented as a template that is applied to a base creature, so in that specific mechanical sense there is no base creature to refer to. However, the fuller description of the bloodhulk in MM4 makes it clear that there definitely was an original creature which is reanimated to create the bloodhulk:
Bloodhulks are corpses reanimated through an infusion of the blood of innocent victims in a dark and horrible ritual.
Creating a bloodhulk requires a ritual of bloody sacrifice culminating in a spell of animation. Most living corporeal beings can be made into these horrors.
You can create bloodhulk warriors [sic], giants, or crushers based solely on the size of the corpse you wish to animate: A Medium corpse is required for a bloodhulk fighter, Large for a giant, and Huge for a crusher. Smaller and larger corpses cannot be made into bloodhulks. The creation of a bloodhulk changes the original corpse too much for it to retain most of its original features.
That last justifies why the bloodhulk statistics derive solely from its size, rather than applying a template; the process simply changes the original body so much that its original features are no longer relevant.
Nonetheless, there clearly was an original creature that has been reanimated, so any effects of awaken undead which refer to the typical living creature of its kind must be taken to refer to the kind of creature that provided the original corpse - the spell description never specifically refers to the concept of a "base creature". Moreover, it is stated that most living creatures can potentially be animated in this way, so for a bloodhulk of unknown origin, it's really up to the DM to decide what the original creature was.
The simplest solution would probably just be to treat such bloodhulks as originally human - after all, humans can be found pretty much anywhere, they come in large numbers and most of them are no good at fighting, so they're readily available subjects for necromantic purposes. Of course, for bloodhulks that have been created by the PCs, this is a non-issue, since they should be well aware of whatever kind of creature it is they just murdered to perform the ritual.