Probably not, and hybrids between orcs and other things probably aren't as much of a thing as you suggest.
As far as I remember, it was never confirmed, in-universe or out-of-universe, that Orcs were descended from Elves. It's just one story, and <PERSON> often emphasises that nobody but <PERSON> their creator really knows.
Unfinished Tales says that another theory is that they're descended from the Drughu or Druedain, a strange sort of offshoot of humans whose descendants appear in Lord of the Rings as the "Wild Men" or "Woses" of Druadan Forest.
The Uruk-hai do seem to be part human, though the idea that they're literally human-orc hybrids isn't entirely confirmed. <PERSON> speculates about it:
It is a mark of evil things that came in the Great Darkness that they cannot abide the Sun; but <PERSON>'s Orcs can endure it, even if they hate it. I wonder what he has done? Are they Men he has ruined, or has he blended the races of Orcs and Men?
And <PERSON> later refers to them (to <PERSON>, who's been telling him about <PERSON>) as "half-orcs":
"And there were battalions of Men, too. Many of them carried torches, and in the flare I could see their faces. Most of them were ordinary men, rather tall and dark-haired, and grim but not particularly evil-looking. 247
But there were some others that were horrible: man-high, but with goblin-faces, sallow, leering, squint-eyed. Do you know, they reminded me at once of that <PERSON> at Bree: only he was not so obviously orc-like as most of these were."
"I thought of him too," said <PERSON>. "We had many of these half-orcs to deal with at Helm's Deep."
But as far as I remember it's never confirmed whether these people were literal hybrids between humans and standard orcs or whether they were humans "corrupted" in the same way as elves (or Druadan, or whoever) hypothetically were. <PERSON> seems to use orcs as somewhat allegorical for humans gone to the bad, so from the story's point of view the distinction wasn't that important.
The small snaga orcs being descended from hobbits, though, is one I've never heard of that I remember. Lord of the Rings just talks as if some orcs are naturally smaller than others. (The orcs, or rather "goblins", of the Misty Mountains in The Hobbit vary a lot in size, too.)
So, hypothetically, a wicked being might be able to create an orc-like creature that's part dwarf, just as <PERSON> creates orc-like creatures that are part human. But I don't remember any mention of any such thing in The Hobbit, The Silmarillion, Unfinished Tales or Lord of the Rings. 88