Instead of having one module provide both APIs, you could provide a new module for the new API and either use the old module under the hood, or refactor the common code out of the old module and both variants of the module use the worker module under the hood.
If your module is OO (::new implies it is) provide a different constructor for each API variant. Your module code can then use any applicable common code and people get to choose to use the new API if they want.
Perl is the programming world's equivalent of English
