Optionally Catch Exception If Not Going To Be Caught By Calling Routine?

I want to write classes with methods that perform JDBC operations that throw SQL exceptions. For many of the methods, I'd ideally like to be able to have them catch exceptions and just send them to a standard Logging system "IF" the code that calls the methods is not going to catch the same exception. However, I'd like the "option" to have code that calls these methods catch the same errors if I want to but not "Require" the calling routines to catch them.... so I don't want to declare the methods with a "throws" that would require all calling code to Try/catch.

For some background, the logic behind what I'm looking to do is that there will be lots of places where these classes and their methods may be used where the code is basically "throw away" scripting code where just having error logs generated is more than sufficient. However there are also places I want to use the same classes/methods that I would want to handle the exception differently. So, for at least half the places I want to use these methods, there's no good reason to require cluttering the calling code with Try/catch, but when I DO want to handle the exceptions, I'd like them to get passed up to the calling routine so I can handle them in a way that is appropriate for the calling routine. Does that make sense?

I guess I'm kind of looking for is the ability to "override" the catch of a called method "IF" I want to but to treat the method as though it doesn't throw any exception "IF" I don't want to override the called routines catch logic.

Is this possible?