A cockaroach is muktza machmas gufo like most animals and may not be moved on Shabbos. It is not considered a graf shel raye because it is not suficiently disgusting and does not bite.
However, like all other muktza items it may be moved using a part of the body other than ones hand, but kicking the roach could kill it which would be a different problem. The better alternative would be what you mentioned, to sweep it away. This is tiltul min hatzad and is permitted.