As far as I know the issue of being able to selectively select where story Project HTML files are stored when using the install-able release of the Twine 2 application has not been resolved yet.
A little technical background.
The install-able release of the Twine 2 application itself will run from a remove-able storage device like an external hard-drive or a thumb-drive. The issue is how the install-able release determines the location/folder of the story Project HTML files.
1. How the story Project HTML file location is determined.
Based on the code in the Twine 2 project's twinejs/src/nw/directories.js file it uses the osenv.home() function to determine the base path of location the files will be stored in, it then appends to that base either "Documents" or "My Documents" (in the relevant language of the end-user) to determine the documents path, and it finally appends the equivalent of "Twine\Stories" to the documents path to obtain the location of the project files.
2. How the osenv.home() function determines the base location.
Based on the code in osenv project's osenv/osenv.js file it uses the osHomedir() function derived from the os-homedir project to determine the home location.
3. How does the osHomedir() function determine the home location.
Based on the code in the os-homedir project's os-homedir/index.js file there is a hierarchy used to determine the home location, and this is where things become a little complex because the hierarchy depends on things like which Operating System (and version of the OS) the end-user is using and how they have the environment of their OS setup.
Basically it is based on a set of Environment Variables which store the paths to folders, each of these Environment Variables may not exist which is why the code uses a hierarchy, and if none of the Environment Variables exist then the folder the Twine 2 application is being run from is determined to be the home location.
4. If you temporary override the value of first Environment Variable checked for your particular OS then you can force the Twine 2 application to use a different home location, which in turn will influence which "Documents\Twine\Stories" folder (in the relevant language of the end-user) is used to store the story Project HTML files. How you do this depends on the OS being run.