I was contemplating moving my DirecTIVO to a different shelf (a few feet above where it currently sits), but it appears the cable coming in through the wall is not long enough.

Do I have a tech come out to rewire it, or is it something I can do?

I'm guessing that is just coaxial cable (probably RG6) coming in from the wall, and, if so, you can just use one of these along with an extra piece of coxial cable to achieve the desired length. You can probably find the connector and the cable at Home Depot or Lowe's (they'll cut a piece of cable of the length you want from a huge spool).