Jack,
If I remember correctly there is a heater register in or near the desk. It is fed by 2 heater hoses that end up at the Hurricane. If you can access them, you may be able to run your new cable along the path of the hoses to access the basement. If not, the cutout will give you access the to the bottom of the sub-floor. You should be able to drill through that with relative ease/safety. You may want to consider running your cable out of the basement via one of the bay doors if it isn't going to be in place for an extended period of time. The gasket should have enough give to accommodate it and allow the bay door to still close.
Once in the basement, a better option may be to run the cable to the water bay and mount a connector the bay wall or just have the cable coiled up there. Then you could access the outside via one of the existing access points in the floor.
Steve.
