Being a Dwarf isn't great--I think Transmuters prefer to be human--but you work with what you have. The extra HP can allow you to take a single hit from an Animated Armor that you wouldn't otherwise be able to, that's probably the biggest advantage. I wouldn't focus on health; attack is still preferable when you're buying items in the dungeon. Namtar's Ward is a good prep if you have it; otherwise, try Dwarven Gauntlets or maybe even a Fine Sword. Prep a Compression Seal so you can carry more stuff into the cursed realm with you.
Transmuter is really not an awful match for Cursed Oasis. One of the big challenges of this dungeon is that in the cursed realm, you don't have access to the overworld goodies you need. With Transmuter, you can LEMMISI a bunch at the beginning to find the important stuff: glyphs, altars, boosters, maybe a good shop item. Because Spirit Sword gives you a single big attack, GETINDARE and WEYTWUT are uncommonly useful. CYDSTEPP sort of works too, I guess. After you've got what you need, convert LEMMISI and use that big attack (hopefully with first strike; possibly with fireball support) to drop a level 3 monster. Take this strategy of converting a glyph and then hitting a monster hard as far as you can; this should give you lots of bonus XP and conserve popcorn.
General Cursed Oasis advice: Manage your popcorn carefully. You need it for fighting Animated Armors, for midfight level-ups, and for removing curses strategically to make a trip or two back to the normal realm to pick up boosters and shop. Bandits are by far the easiest monsters to kill, but they curse you. An ideal board has lots of bandits in the level 6-9 range so you can get a couple levels using mostly them immediately before tackling the first boss. Higher-level Animated Armors have relatively low HP, so sometimes with the help of a mana potion or something you can fireball them to take off a level of death protection, ignite the Burning to take off another, and then they're weakened enough that you can survive a hit.
The WONAFYT glyph is helpful in this level if you find it, because it lets you pull Shades out of blackspace without them draining your HP. The Piercing Wand is helpful for lowering the Cursed Shade's resists, as is BYCEPPS, but neither is necessary; it has a very shallow HP pool. The second boss has Retaliate: Fireball, so either spend your mana resources on the first boss or have another glyph available that will allow you to turn mana into damage (CYDSTEPP, PISORF and an appropriate layout, APHEELSIK if you happen to have blackspace left).