A lot depends on the run. First. Your existing coax likely has a 'Break" in the roof. This is so the exposed cable between roof and antenna can be replaced without replacing the entire cable (A very good design)
You can use the cable from the switch box to the roof, but you need to disconnect from the switch box.
RG-59 is normally what you have and that is not really speced for Sat use but the run is short enough you should be able to get away with it. Just figure however many feet of RG-59 you have, Multiply by 5 to get the effective length of RG-6. In mny case the RG-59 Run is less than 10 feet
NOTE: if your RV is "Sat Preped" odds are somewhere near the center of the roof is a buried length of Coax and a pair of 12 volt wires as well.. There may have been a sticker at one time, or a "Vent" (in my case) the wires are under same. Use a cable tracker to find them if you have them. (Will be cables in teh Electronics bay labeld "SAT".