So you'd like to take a sunrace COTTERED cartridge BB, pull off the pressed on english threaded cups it comes with, find a (used preferably) Shimano cartridge BB with Italian threaded cups, pull off the pressed on Italian cups and install them on the Sunrace cottered BB unit?
I'd find a bicycle co op or the LBS and have them give you a scrap shimano cartridge BB (any thread) to see if the ID of the cups will fit the sunrace. If it's good, or at least close enough to shim or bore, then start looking for an Italian threaded one.