Hi - cotoneasters will flower and fruit on the growth it makes next year, so pruning is safe now, or you could wait and enjoy the berries over winter and do it at the latest just after you see new growth start next spring.
I had a nice upright form against a wall - I pruned it into an espalier which kept it tidy and also encouraged tonnes of berries every year. If yours is too big or unsuitable in position for that, try to keep it in arching tiers (if unsure, look up a picture of viburnum mariesii to see what I mean) but definitely avoid making it into a dumpling. It looks unnatural and odd shaped like that, and becomes just a blob, instead of a nice shaped thing in its own right...
B xx