All I do is when I am doing the dishes, I partly fill the bottle by submerging in the sink replace the cap and shake well. Then rinse with tap water. If there is any more cleaning needed I use a small soft bottle cleaner brush and I flush the sipper caps well with tap water. I dont use the Sigg brand, but mine are lined like the Sigg's. The Sigg uses a better lining, but the dish detergents Ive used havent had any negative effects.
Sigg have there own cleaning kits with a brush and the 'special cleaning detergent' to prevent lining damage but I cant see any advantage. Especially when they advertise how tough their lining is compared to other brands <img src="/images/graemlins/smile.gif" alt="" />