Is Dectomax safe for dog skin issues? Should I neuter my male dog?

A full and complete diagnosis of the cause of the rash is required - I would recommend referral to a dermatologist. Dectomax (doramectin) is an anti-parasitic agent used to treat mange, fleas and roundworms - if Oreo has mange mites confirmed on skin scrapes then he would require treatment for them but not necessarily by injection (although the injection is often used without side effects, there are also oral and topical options available which cover the same mites and are licensed for use in dogs). I would not recommend castration as a solution to the skin issues unless a hormone-responsive condition has been diagnosed or no other treatments have had any effect as it would be a very rare cause and indeed castrated dogs can develop a different set of skin and coat problems