Perhaps the question can be resolved simply by looking at meanings of necromancer and necromancy that Tolkien would be most familiar with. After all, I do believe he knew the OED a bit better than the Merriam Webster on line dictionary.
The first uses of the words recorded in the OED focus more on communication with the dead rather than raising of the dead as spirits to be commanded. In fact, the first meaning given implies just a general reference to wizards and magic rather than to any zombie like animations.
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Originally Posted by OED, necromancer
One who practices necromancy; one who claims to carry on communication with the dead; more generally, a wizard, magician, wonder-worker, conjuror.
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Originally Posted by OED, necromancy
The pretended art of revealing future events, etc., by means of communication with the dead; more generally, magic, enchantment, conjuration.
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One can always take up the OED for the assumptions behind its definitions (viz. the use of "pretended" in the second definition here, as the early employers of the word could quite well have believed in the ability) but it isn't until a usage from Swift that the idea of animated dead acting in this world appears in the quotations explicitly (if I'm reading the tiny print in my microreduced copy correctly.)
So, it is quite possible that Tolkien meant simply a wizard of the dark arts, one who communicates with the dead, even to the point of swearing oaths with them, in order to gain some advantage of knowledge, rather than to any possiblity that Sauron was press ganging the dead into his service as was the wont of the British navy.
Those with a taste for the living dead or the more ephemeral ghosts might of course apply their own thoughts, but perhaps Tolkien in this case merely meant a wizard of the dark side.