It's not possible to be a Maia but not be one of the Ainur, as all of the Valar and Maiar were Ainur.
We're certain that Shelob is an offspring of Ungoliant, so the key question becomes: "what is Ungoliant?"
IMO there's too much of a tendency to declare that any unknown type of being must be a Maia. The Valar and Maiar were not the only spirits in Ea; there are at least two other examples from the Silmarillion, first of all those in the first conflict between Melkor and the Valar (from the Ainulindale):
But Manwë was the brother of Melkor in the mind of Ilúvatar, and he was the chief instrument of the second theme that Ilúvatar had raised up against the discord of Melkor; and he called unto himself many spirits both greater and less, and they came down into the fields of Arda and aided Manwë, lest Melkor should hinder the fulfilment of their labour for
ever, and Earth should wither ere it flowered.
And secondly those who became (among other things) the Ents (from Of Aule and Yavanna/Of the Ents and the Eagles):
When the Children awake, then the thought of Yavanna will awake also, and it will summon spirits from afar, and they will go among the kelvar and the olvar, and some will dwell therein, and be held in reverence, and their just anger shall be feared.
Here both Manwë and Yavanna are capable of summoning spirits, so why should Melkor (who was in the beginning at least as powerful as Manwë) not also be? Furthermore, if Melkor is capable of corrupting Sauron and the Balrogs into his service, why should he not be capable of corrupting other spirits?
The last writings on Ungoliant were from the "LQ2" revisions to Quenta Silmarillion, and first of all deal with her origin:
In Avathar, secret and unknown save to Melkor, dwelt Ungoliante, and she had taken spider's form, and was a weaver of dark webs. It is not known whence she came, though
among the Eldar it was said that in ages long before she had descended from the darkness that lies about Arda, when Melkor first looked down in envy upon the light in the kingdom of
Manwe. But she had disowned her Master, desiring to be mistress of her own lust, taking all things to herself to feed her emptiness.
This is mostly standard stuff, but new here is the "but she disowned her Master" statement. Who was that Master? Melkor, of course:
...such darkness as in her famine she could weave was no defence against the eyes of Melkor, Lord of Utumno and Angband.
'Come forth!' he said. 'Thrice fool: to leave me first, to dwell here languishing within reach of feasts untold, and now to shun me, Giver of Gifts, thy only hope! Come forth and see! I have brought thee an earnest of greater bounty to follow.'
So that much is clear: Ungoliant was some form of being who was originally corrupted by, and served, Melkor, but had struck out on her own at some time in the past.
Key to Ungoliant's origin is a very specific point in time, so I'll emphasise it here: "when Melkor first looked down in envy upon the light in the kingdom of Manwe". The important word here is light, and that allows us to pinpoint her to the time after the Lamps were raised (Of the Beginning of Days):
...far off in the darkness he was filled with hatred, being jealous of the work of his peers, whom he desired to make subject to himself. Therefore he gathered to himself spirits out of the halls of Eä that he had perverted to his service, and he deemed himself strong.
And seeing now his time he drew near again to Arda, and looked down upon it, and the beauty of the Earth in its Spring filled him the more with hate.
Lending further weight to the claim that this was the time, we see the words "jealous" and "looked down" here. So this was when Ungoliant entered the world.
Knowing from above that Melkor was Ungoliant's original Master, we therefore reasonably conclude that Ungoliant was one of those "spirits out of the halls of Eä that he had perverted to his service" (and Melkor therefore is capable of summoning and corrupting spirits), and that she's no more a Maia than the spirits Manwë or Yavanna summoned.
And therefore nor is Shelob.