Jenkins path to git Windows master / Linux slave

I have a Jenkins master on Windows which runs some Windows builds.

The git client plugin in configured with a fixed path to git as "C:\Program Files (x86)\git\bin\git.exe"

I've now created a Linux slave, but when I run a job on there, it's trying to run the command "C:\Program Files (x86)\git\bin\git.exe init", and obviously fails.

Is there a simple solution to this? I think I've resolved it already by modifying PATH on the Windows master, and the fixed path to git is now just "git" so would work on both OSs.

Is the "correct" way to resolve this for Jenkins, or is there another/better way to do this?

Thanks.