Nice cover. I have a number of similarly torn covers and face the same dilemma you have. I store them in a box, figuring they are already damaged and no further harm can really come to them. In your case, however, I would want to keep the cover in a sleeve so as to protect the campaign stamp and not risk any further damage.
Although I don't possess this Cinderella (wish I did!) I downloaded this Cinderella/Poster Stamp from the Library of Congress web site, I believe, that also addresses the Women's Suffrage movement. Interestingly, this example seems to have been postmarked New York, NY in 1903, (probably placed next to a stamp in the upper right hand corner of the envelope).

As I have never seen this one before other than from a library/museum web site, I wonder if it's a common or rare piece? Anyone know?