The first rule of "How to wrap a subroutine": don't name it the same as a Perl built-in function (without a really good reason). This is such a bad idea! You are digging yourself a pitfall and seeding it with nasty booby-traps. The most likely ultimate result is a bamboo stake up a very sensitive part of your anatomy. Please call it something like  delete_file_and_zip() so I can sleep peacefully tonight.

Otherwise, the logic of the function looks ok.