I have an executable that is started by a windows service, this program will be run on a customers machine and will need to connect to a remote share to perform a particular
Why can't you use another account? There is a network service account built into Windows, specifically for services that need network access.
Anyway, be very careful when having a service start an exe.
If the write access to the folder with the exe is not disabled, a user can replace that exe with (for example) cmd.exe. The next time the service tries to start your exe, voilà: A command shell with system rights!