Thanks for the info folks! I did ask the developer for further information, and they did manager a solution for me.
On one of their support pages for this activity they published the install command that works below:
"LighthouseStudio_9_15_0_1_Setup.exe" /VERYSILENT /NORESTART /TASKS="uninstallpreviousversionsautomatically,excelplugin,desktopicon"
I asked them how can I adjust the first TASK there to do the opposite (i.e. not uninstall the previous version), and they could come up with the syntax I needed below by adding a "!" in front of it:
"LighthouseStudio_9_15_0_1_Setup.exe" /VERYSILENT /NORESTART /TASKS="!uninstallpreviousversionsautomatically,excelplugin,desktopicon"