Gentle shampoos (and I can't imagine yours NOT being gentle) are usually fine. I use some of Jhonen's shampoo, or Dr. Bronner's if I wash handknits in something other than Soak (and will make the mental note to wash in something non-Jossie-caustic when we are going to be in your general physical vicinity).
Hannas tend to do just fine in the wash. I've never (knock on wood) had issues with machine washing them. Just block and air-dry any knit items and you should be fine.