Did your vet do a skin scraping to determine the diagnosis of mites? Some vets don't know much about hamsters and they shouldn't prescribe for mites without testing first as it could be unnecessary treatment and all medications can create some toxicity within hamsters. So important to know it is really needed.
Fur loss can be caused by a number of things, and particularly as hamsters age, or in warm weather like now, as they can moult a bit/shed their coat. Our Syrian looked very mangy this time last year, but his fur all grew back!
If your vet didn't test, then I'd suggest googling for exotic vets in your area - they know a lot more about hamsters and some even specialise in "small furries".
So suggest getting a skin scrape to determine if it actually is mites, before any further disinfecting, and as you say that could be tricky (but not impossible!) with a wood cage. I would think wiping the wood down with pet disinfectant would do the trick if necessary but could be an idea to use a fairly odourless one like this one (recommended to me by Cypher
). As the wood could absorb any scents for some time.
https://www.ebay.co.uk/itm/Safe-4-pe...0AAOSwIhxZayY5