What you are proposing should work well. Don't forget to make a fresh backup before starting.
If you do not wish to reinstall skins, plug-ins, and visualizations then before uninstalling make a copy of the folders:
C:\Program Files (x86)\J River\Media Center 19\Plugins\
C:\Program Files (x86)\J River\Media Center 19\Data\
C:\Program Files (x86)\J River\Media Center 19\Skins\
C:\Program Files (x86)\J River\Media Center 19\Visualizations\
Then after installing in the new location, overwrite the new location with the above folders.
Or, a simpler approach which some people may not like, but ensures you miss nothing, is to make a copy of
C:\Program Files (x86)\J River\Media Center 19
Then after installing the same version in the new location, overwrite everything in the new location.
With both approaches, I think you may have to rebuild thumbnails. If this is a problem I may be able to remember how to avoid it if I think a bit more.