So an Aslan could use a SMG if MGT had included one!
...and might just snatch yours out of your 'primate' hands.
Is that what you are saying?
Aslan hands are probably better for snatching stuff than human, and less susceptible to directional leverage. Probably not quite as good at finer motions; IMTU the central thumb leads to a slightly larger minimum unassisted manipulation size (They reach for the tweezers for slightly larger stuff than we do). Hence larger buttons, viking period style large-needle stiching being both functional and decorative simultaneously, fewer concealed stiches. On the other hand (pun intended) claws allow easier operation of small and recessed switches.
As for using a human SMG, I'm certain it could be managed... the penalty provided for aslan weapons in human hands and human weapons in aslan hands is rather notable, but does imply they CAN be used. (See AM Aslan)
Some tasks woud be done in a different manner, but with no less (and no more) difficulty, eg: loading a revolver with loose rounds. Where the primate hand can hold loose rounds in palm, and thumb-push them to oppositional grip with the index finger, the aslan hand won't carry as well, but I can see 6 rounds, 3 each slot, being pushed forward with a thumb into the cylinder's chambers. (I knew a guy who loaded pistol clips that way, but with the primer away from the palm; four rounds between index and middle, and four between middle and ring, lifted out of the box in those groups.)
The central thumb does make the aslan palm less useful as a carrying place for small items and liquids.... it is a series of small usage differences.
If you ever want to play around with functioning with claws, go buy some cheap finger-pics (typically about a $1.50 each), and go through the day with them on upside down. (They are normally worn with the ramp under the tip; instead put it over the nail.) Doi it for a day or two, and you will find subtle differences in how you do things.