This is not a problem I have really run into more than once, but I can't recommend the tools that penguin mentioned highly enough.
I have a Fein Multimaster 250, and it is the perfect tool for this job - and a good number of other inconvenient cutting jobs lock related and not.
The best part is, if you are clumsy, it is extremely difficult to cut yourself with. The oscillating drive allows the blade to cut through wood or metal or plastic, but then if you accidentally go into your skin, it wont break the skin. (don't try this at home?)