For other readers, you must be very careful reducing the length of some cables because cable loss has been taken into account by design. For power as an example the cable loss is many times taken into consideration and if you remove that loss, the voltage can enter a unit higher than allowed and smoke something. Same goes for many of your signal lines. So when in doubt ask; just as Sheakx is about his install.
Sheakx
Officially the shortest cable is 5 meters (~15 feet). Since the cable (power/data) blends together it might be very tricky to cut back the cable and do it correctly (never seen done/don't recommend). You might want to consider ordering the radar with the correct 5 meter cable (p/n SN3-000-000-68) instead of the 15 meter that comes with it and then just keep any extra cable coiled someplace. If you really want to cut up a new cable cable, it might be better to order the older 5 meter DRS cable (like the DRS4D uses, p/n SG3-000-000-79) that is much easier to cut back because the power and data are separated the entire way. You would have to remove the pigtail cable from inside the NXT and wire the cable direct into the dome. Using that, you "should" be able to cut the cable to the 10 feet you are looking for (at 12V).