Building paper soaked and rotted
I've got a bathroom that has water damage in one of the walls of the shower. The water got into the wall from a window seal inside the shower and I believe it came from inside the shower and not outside the house. Anyway we pulled the tiles and sheetrock off and found that everything under the windows was soaked. The insulation was dripping and when we pulled it out some of building paper came off with it. This appears to be the only water barrier that was there (about 1.5 inches of stucco, chicken wire, building paper, insulation, then sheetrock). A few of the 2x4 studs are damaged as well but most look like they're in good condition.
The house has a stucco exterior and is about 20 years old. My question is how do I go about fixing this? I'd like to replace the building paper so that I get a proper water barrier but in order to do so I'd need to remove all the studs from the wall (about 5ft of wall). The studs are attached to the stucco with small nails and staples so I think I could remove them with some care. However I'm concerned about the effect this would have on the stability of the wall (i.e. would I need to re-attach the stucco wall to the 2x4's and if so how?) Are there any other options that would not require the removal of the studs?
The wall is on the East side of the home which is the most protected from the weather however we do get a fair amount of rain during the winter time.
Thanks in advance for your help,