IIRC there is a limitation on the number of blaster-style projectiles that can be created when a gun is fired at a time, so a shotgun would probably either have the hitscan bullets of the FA versions or have a more limited number of blaster bolts (i know 3 at once is possible, idk what the upper limit would be).
As for competitive/sweaty gameplay, defense is already very easy compared to offense usually, so the shotgun would need to be fairly limited at range or against multiple enemies to prevent corner camping metas. I think the damage of each individual shot would have to be quite low or the rate of fire slow enough so that very quick peeks with a shotgun wouldn't be overpowered if you were camping in a corner. I would be most interested in a shotgun alternative or upgrade to the bowcaster to emphasize the wookiee's role in taking space and close range destruction, countered by snipers and grenades to prevent the wookiee from running up.
Another interesting weapon design, effective at all ranges, would be a hybrid spread and slug shotgun, where clicking would shoot a spread of low damage projectiles like a shotgun, but charging the shot would reduce the number of shots but increase their damage and accuracy until it converged into a single, accurate charged shot.
Agreed that there's lots to explore.