So, as I said: set up ssh-agent on the box with the identity, let that hold the passphrase guarded key for you, and it'll just work (presuming said ssh-agent is running, which may require some form of manual intervention if/when it restarts to unlock the identity for it). It's still not a Perl problem.

If you're dead set on making it a Perl problem you'd want to look into something like Expect and let that drive your scp, but then you'd need to embed the plaintext passphrase somewhere in code and you've taken two steps back security-wise.