The problem you will quickly run into is that dwarves from a folklore standpoint started out in an ambiguous fashion. They started out in Norse mythology and other similar mythologies as a fey like spirit of earth. They dwell in another realm known Dwarfheim and were known for being master craftsmen. They made most of the gods weapons and armor, including Thor's hammer Mjolnir, and in one legend one crafted a magic ring of great power. This particular legend is the one that went on to inspire both Wagner to write his opera the Nibilungenlied, or "The ring of the Nibilung" and Tolkien with the Lord of the Rings. The problem was, pre-Tolkien, who more or less standardized the modern Dwarf, the terms dwarf, elf, and gnomes were often used interchangeablely, and were basically just all lumped as the same creatures (and debatedly a racial slur for Jewish people, though that is a whole other conversation). Elves were more those that lived in the woods, while gnomes were spirits of earth, and the term dwarf often got used for both.
The issue you run into is that while d&d is great for terminology, sometimes they use different lore or terms for things from traditional folklore. Gnomes basically ARE the "fey dwarves" you seek. Wild gnomes have a more traditional folklore feel, but either rock gnomes or (especially) Svirfneblin (they are in the monster manual and racial stats are in the sword coast guide) are what you should look too.
That said, as others have pointed out, letting the dwarves live in the underarm is not a bad idea as well. Do not belittle the races ability to live entirely underground for most or all of their lives. Alternatively, if you still wish for a more alien extraplaner type thing, take the idea of the elemental earth plane and look up Dwarfheim in Norse mythology. I'd populate it with dwarves, gnomes, and earth elementals, as well as other creatures that fit thematically (purple worms should be their alpha predator type thing). Honestly anything that is underdark works.