Why don't you just deploy it centrally with an installer that is not bundled with 3rd-party software?
As Pat mentioned, there are alternatives out there. I sympathize with admins and I know our team wants help reduce your workload, not increase it.
First, head over and fill out the form for Flash Player distribution. While you could look into SCM/GPO based distribution, the best solution imo is leveraging our background updating system. Please see this post for more details:
Additionally, check out page 19 of our Flash Player Admin guide.