I'm sorry to hear your little ham is under the weather. As you've seen your vet, I expect s/he has excluded other causes of itching such as mites, cutaneous cancers or substrate/bedding allergy. I have heard of mice having extreme itching problems which is thought to be related to higher protein content foods, but I haven't experienced/heard of this in hamsters.
What is Ollie's food intolerance to? There is no specific 'hypoallergenic' hamster food so you would need to find/make a food without whatever he is allergic to. I had a hamster with a gluten intolerance following a bowel infection (which manifested as diarrhoea rather than itching). We identified this by using an exclusion diet - starting with just boiled chicken and rice for a week (no extras, no dog biccies etc) which entirely resolved her symptoms and then reintroducing one component at a time and monitoring the results. I ended up making her a food based on rice flakes as all commercial foods have gluten in.
I would recommend supplementing Ollie's food with a vitamin mix, such as Dr Squiggles, if he isn't having a commercial hamster mix.
In terms of recommending a vet, it would help if you mentioned the rough area you live in, e.g. county/city/state and country
I hope he feels better soon.