From the template (I've bolded the important part):
Quote:
Type: The creature's type changes to undead. It retains any subtype except for alignment subtypes (such as good) and subtypes that indicate kind (such as giant). It does not gain the augmented subtype. It uses all the base creature's statistics and special abilities except as noted here.
So no, it doesn't have the daemon subtype as that's a subtype that indicates kind.
For an example, a skeletal Hydrodaemon would be Undead (Aquatic, Extraplanar), while a skeletal Ceustodaemon would be Undead (Extraplanar).
It looks to me like you'd keep
Acid, Air, Aquatic, Cold, Earth, Extraplanar, Electricity, Fire, Gravity, Incorporeal, Mythic, Native, Shapeshifter, Swarm, Time, Water
and not much else.
