If nonrusty skin laceration, can I just clean it and put on bandaid?

Yes. For small cuts, apply direct pressure for 10 minutes to stop bleeding. If this is successful, all you need to do is clean the area with soap and water and cover with plain vaseline and a band-aid. Repeat this once daily. There is no reason to use topical antibiotics like neosporin or bacitracin. Repeat daily until the skin heals over. If it becomes red, painful, or oozes pus, see your doctor.