I have come up with the following utility class:
import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.SQLException;
public class MySql
You can throw an exception in your original code upwards, and then have to deal with a possible exception every time you would want to get a connection. Granted, you will not have null issues, but this could end up being more work. However, it does make it very explicit that you have to handle the connection not working, and this could be clearer than simply returning a null.