Can someone with better housekeeping sense than me tell me how to clean this futon/mattress cover that is not machine washable.

[Bryt]

I have an Ikea futon/sofa bed. It has a sprung mattress and a thick white cover that I have realised zips off. Unfortunately, it says not to machine wash it and advises cleaning with an upholstery shampoo. There are two small stains on the mattress cover. They look like water marks - most likely my daughter being careless with a water bottle when using it as a sofa. What's the best way to clean the cover? If I can avoid getting the whole thing wet, I would prefer that, but will upholstery shampoo do the job? Will I be able to rinse it adequately if I just spot clean it - or should I use something else, like soda crystals?

Any help greatly appreciated.