To be clear, Norton is really must an AV engine. It has some rudimentary anti-spyware/malware features, but they really can't compare to a try spyware cleaner tool like the ones mentioned. It's always safe to use multiple on-demand anti-spyware tools -- they all have their strengths and weaknesses and complement each other.
What is definitely NOT recommended, and a recipe for major performance issues, is to run multiple real-time AV products at once. So pick an AV product like Norton for real-time protection, but supplement it with anti-malware tools.