The Annese can tie elaborate knots that melt on a tug. This implies more than adequate dexterity to use tools.
Their awkwardness is probably due an apraxia - a brain deficit that makes it difficult to plan motor actions to complete a task.
In humans, this deficit is usually caused a specific part of the brain being damaged by a stroke or brain tumor.
In the Annese, I suspect that this brain deficit is intrinsic to their normal (at least normal to an Annese) neurophysiological makeup.
Since it is intrinsic to their nature, it's a pretty good tell as to who is Annese. Kind of like the stiff, deformed pinky fingers in the aliens of Roy Thinnes' The Invaders.
I like this idea that the imperfect mimicry is in the brain and not in the hands themselves.
I wondered about why they cannot adequately use tools but are good with knots. There is also a comment in the first novella in the library scene where the use of knotted nets by the Annese is discussed ("and for primitive people the most effective way to fish is probably with weirs, or with nets of rawhide or vegetable fiber", as David opines. Wolfe likes weird puns and I wondered if he intended a pun between a knot and naught, but I still don't know what it could be.