It wouldn't change much:

sub MIME::Lite::new {
    my ($self, %params) = @_;
    ok (exists $params{To}, 'To address present');
    ok ($params{To} eq 'wibble@wobble', 'To address correct');
    ...
    goto $new;   # <--------------
}
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You'd be making use of the goto &NAME functionality (see perldoc -f goto), where your wrapper for Mime::Lite::new() gets replaced on the call stack with the real Mime::Lite::new, which was saved in $new. The goto-ed function is called with the contents of @_. According to the perldoc:

    After the "goto", not even "caller" will be able to
    tell that this routine was called first.
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The consequence of using goto makes your wrapper function, which does the testing, invisible to the script being tested. That reduces the possibility where addition of a wrapper function inadvertantly causes a bug (that only manifests itself while running under the test-suite, making it harder to find), or causes a test to fail that wouldn't otherwise fail.

Does that clarify things?

Cheers,