Then you should be ok.
The issues I have found (I have a DB and a free/paid version) were: 1) making database structure changes; 2) migrating data from the free to the paid database (if the user upgrades). If the DB stays the same from v1 to v2, it keeps the data with no hassles.
Other than that I do just try and test updates thoroughly by having an old one on the phone and then installing the update. And 'cause I am paranoid, I will retest it once I have uploaded the update.
You will need to update the versionCode and VersionName in the manifest. Android uses versionCode to check increments (it's just an integer value that needs to be incremented); and the versionName is only used to indicate to users the version number, but it not a absolute necessity (normally this is the 1.1.2 type format)!
But otherwise users will just get periodic notifications on their phone, and then install the new version.
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