Ok, I tried that and it would have worked, if weren't for the fact that the separate MySQL installer we have runs the MySQL configuration wizard as a sub-process.
This means it tries to pass an updated PATH variable to our application which has not yet been updated.
To get around this problem, I have disabled the "Start application" option from the final wizard page. We have several different versions of the installer (standard, full and express) and this issue only affects the full version where the user has complete control of the MySQL installer. This means that we can never guarantee that the user configures MySQL correctly and consequently cannot guarantee that the "start application" option will work.
For our other installers this isn't a problem as MySQL either exists already on the end system, or we have control of the MySQL installer.
Many thanks for the tips kichik!