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You can Raise Spectres from your Zombies. Those will be Raised Spectres of Zombies, not Raised Zombies. Bonuses for your Raised Zombies will thus not apply to them, bonuses for Raised Spectres will. But you can do it.
What sort of level would the Raise Spectres be? Would they be based off the map you're in? Where you initially Raised the Zombie? Gem Level of Zombie? (If this then would Gem level 20 be Spectre level 100 zombie? O.o )
Level of the Raise Zombie skill is what determines the monster level of the zombies.
Mark, Do these gloves consume (kill) your zombies if you use an offering?
If they're near enough to where the offering is cast, then yes, because they count as corpses.