I wouldn't even take the drywall off & blow in cellulose. If you prefer fiberglass, you can use it to, but cellulose is less expensive & has some characteristics that make it preferable.
When cellulose is paked in a cavity (Like a wall), it is packed to a point that virtually elliminates air leakage, ellimniating most moisture concerns (Air leakage is the main cause of moisture problems. Air carries the water vapor until it hits a cool surface, with a temperature below it's dewpoint, and then condenses. Air leakage control is NOT a vapor barrier issue!).
As far as a vapor barrier, don't worry about it unless the issue is pressed by local codes. Most solid matter are a vapor barrier (Although some not much of one) in that it slows the movement of water vapors trying to go through. With siding or drywall, especially if there several layers of paint, you probably already have the legal perm rate. If not, use a qualifying paint. Remember, the primary way moisture past the wall or siding is by convection,. If that is solved, the reat is minor.