Ok so what you're asking sounds pretty much impossible. Based on what you're asking I'm going to assume you have access to a network which is administered and controlled by someone else. So I guess the obvious and probably somewhat dumb question is, why not just ask whoever admins your network to move the printer, or ask them what it would take to get the printer moved the right way instead of trying to Macgyver your own solution?
Short of that, I probably won't cost as much as you think to get someone to run a CAT6 drop for you.
Short of that, I probably won't cost as much as you think to get someone to run a CAT6 drop for you.