Execute exe file on each server after deploy

Question

I have created a SharePoint solution, i need to deploy a “.exe” file to all of the servers in the farm, so i add the “.exe” to the BIN map folder. After the solution has been deployed, a feature(farm scope) will be activated, and i need to execute the “.exe” file in each server. Now i create a custom timer job to do the job, but the SharePoint timer service is running on Network Service account by default, there will be a permission issue when i execute the ".exe" file in the timer job.

How can i  fix this issue without change the account of the SharePoint timer service, or is there any way to execute the ".exe" file automatically on each server after deploy the solution?