Not sure if I understood your question correctly, but why not store the database location in a simple configuration (text) file in the same folder where the application is.
The first time the application runs, let the user specify the database location with a File Open dialog and store the location in the configuration file. Personally I wouldn't store the whole connection string in this case, just the location and then build the connection string in the program.
What comes to security I'd use a database password for the database and when the database is opened I'd ask the user for the password. I wouldn't store the database password anywhere.
About database password, see
Set Database Password and Unset Database Password[
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