If you have settled on a particular set of tools to access / modify your databases, I would go with whatever extension they expect you to use. This will avoid needless friction when doing development tasks.
For instance, SQLiteStudio v3.1.1 defaults to looking for files with the following extensions:
(db|sdb|sqlite|db3|s3db|sqlite3|sl3|db2|s2db|sqlite2|sl2
)
If necessary for deployment your installation mechanism could rename the file if obscuring the file type seems useful to you (as some other answers have suggested). Filename requirements for development and deployment can be different.