Cover the back of the canvas with a blotting paper. Change the blotting paper until the canvas is dry. Learn more about how to treat water-damaged paints in this video. Cut the blotting paper according to the inner dimensions of the stretcher frame.
You can insert blotting paper (or even a kitchen towel) between the canvas and the stretch bars. Since the wood in the elastic bars dries slowly, it will not continue to introduce moisture to the canvas when the paper is added. Removing stains from works of art on paper is an extremely complex process and how to do it depends on the paper, ink, printing process, assembly and much more. The best thing to do is to leave your fingerprints alone if you don't want to seriously damage them.
Bleach or hydrogen peroxide will deteriorate the paper if not used with the correct dilution and then thoroughly washed. Washing requires extensive testing to ensure that the process does not modify paper and ink, and these tests require training not only in art, but also in conservation and chemistry. Paints and their composite materials will have their own individual response when exposed to damage caused by moisture and water.