Hey so I've been still practicing my flintknapping and here I have an example of a pretty simple unifacial obsidian adze hafted to a very short handle.

It's a very short adze that is about as heavy, but far shorter, than my copper adze. It is about a foot long and that's it I didn't take a picture of the head I flintknapped so I apologize, But it is a very simple unifacially modified flake that broke off of a large piece. I simply retouched the back to make it flat and dulled the edge slightly (a razor sharp edge is a breakable one for wood working). The haft is a mostly straight branch with a shelf carved into it to hold the bit. A hole was also drilled through the stick that is unfortunately covered by the hide in this picture. Artificial Sinew was then strung through that hole around the bit and, because it was quite ugly, that was then wrapped with some hide to both provide extra structural support and also hide the mess of string. The attachment is solid and doesn't really move or twist, and after beating it against a dowel rod, it has yet to budge at all so that's a good sign

I did use a metal saw to help cut things as, while I could have used my copper adze, wedges/chisels or obsidian saws that I do have. My time has been particularly limited and my wrists, particularly painful, so I went with the faster method that was easier on my hands and carpal tunnel afflicted wrists.

The hole was drilled with an obsidian bit though, just simply took a series of small flakes and slowly twisted them through most of the way of the wood before using a hot piece of copper wire to burn through the rest to make a small, evenly wide hole throughout the stick
Which was actually pretty fast, it was about 30 minutes of messing with little flakes and about 2 with a very hot copper wire
Of course I do apologize as everything is covered up, I don't want to disassemble it as the assembly of everything was actually pretty tedious
I am hoping to take it out before I return to university to do some woodworking on greenwood, hopefully it will hold up well but only time will tell.

As for the DragonScape lore
Adzes are pretty useful and accessible woodworking tools for drekir and are made out of a lot of materials. Copper (I have made a copper adze already), ground stones, ground slate, bone, chitin, and knapped stones and glass are all good materials for making an adze blade out of

Adzes also ergonomically work a lot better with drekir overall than a horizontally swung axe
And a smaller adze like this might be a lighter duty adze, it won't be pecking down trees so much as its for smaller tasks around the den, such as shaping handles or atlatls, shaving down chunks of wood for kindling, etc. In a pinch it could probably chop down smaller trees but its gonna be a bit tedious but it will get the job done in all likelihood
It might also be seen as an adze for a group of travelers, a trader caravan both needs tools to get by between communities and would prefer them to be portable, they aren't exactly in a need of large lumber so a small adze for cutting down smaller saplings, shaping wood stakes, or breaking up pieces of dead wood for a campfire are all really useful things
and of course while copper, or ground stones, would probably be generally preferred for making adze heads, knapped stones and glass are not at all unheard of and for cultures that rely more on knapping stones than grinding or using other metals, stones, bones, etc. them it would probably be the go to
Most adzes would probably be like the one above. Not complex, thin bifaces but rather chunky unifaced thick flakes that will do just fine, even if they aren't the prettiest thing. Drekir don't have long flintknapping traditions nor is pretty the thing they always want for a utilitarian day to day object.
And when it eventually dulls beyond usefulness, they will likely retouch it or just throw it away and make another head to attach to the handle.