If you're not worried about his skin, what is it you're asking for advice on?
Having said that, although stress can trigger problems, it's important to still manage them rather than using that as a cause for dismissal. None of my rats have ever had dry itchy skin in old age. What makes you say that you know he doesn't have mites? If his symptoms are ones that would make you think mites in a younger rat then I would treat him - it's probably the first thing a vet would recommend too. For one thing, rats get mite flare-ups if their immune system dips for any reason, and one of the key causes of that can be stress
Unrelated to your old boy, but is your 8 week old getting company of another kitten?