I know that the Linux server does not run a ssh server, it only runs an ssh client.

Are you sure about that? I'm not a Linux expert or anything, but I believe that by default, most Linux distributions (for sure Red Hat) have the ssh server installed and running. Also, I believe (but could be wrong) that the SFTP service is running under the ssh service. In other words, if the ssh service is turned off, then the SFTP service is off too. Now to get off this side trail of thinking out loud...

Anyways, it sounds like manually you're using an SFTP client. In that case, using something like Net::SFTP, Net::FTPSSL, or Net::SCP might do the trick, depending on which protocol you're actually using. I'd suggest testing it out in a separate script to see if you can transfer a file. Once you've got the kinks worked out, then you can decide if it's easier to incorporate it into your existing script or keep it separate.