Cookie Quandary

I wrote some cookies for a whole bunch of site admins, but failed to set the path, so all the cookies are set to '/admin', which is not going to work for everything they need to do. They are also too long, set for 6 months. I need to correct both issues, so I changed it to write cookies to '/' for 72 hours. I've checked my Safari, and I see that I have both cookies set: A long one for '/admin' and a short one for '/'. I'm worried that once the admins' short cookies run out, their browsers will pick up the longer lasting value for the '/admin' version of the cookie. I want to kill everyones' '/admin' cookies, but I'm worried that some browsers might erase both cookies if I do this. Does anyone know if I can safely kill the '/admin' cookie without risking deletion of the '/' cookie?