Hello, i have four boys and this is what ive found.
When we got our second hamster our first didnt seem botheres but the new hammy seemed a little tetchy. However, when he gets teeth chattery we just move him out the room for a night or so and he calms down,
All the others are fine, they are a little distance apart from each other but you wont beable to irradicate all smell traces so they will get used to it.
My friend had our boys for a week and had them in the same room as her two girls...all my boys were going very mental and indy even bent his cage bars back!
so in summary-
i would keep to single sex unless housing in sep rooms..if they cant smell the temptation likely to be better.
washing hands yes but after a while they will be fine, all my boys are used to each others smells now and dont seem bothered so just come out onto my clothes and things fine
keep cages a little apart just so the smell of another hammy is directly invading their space.
this all may eb wrong but it is from my own experiences
xxx