Dunno about the coastal route (we've never taken I-77 to I-26), but Mapquest shows it's about an hour quicker than the I71-75 route.
If you'd rather take the 71-75 route, you should have no problems. You'll be travelling the mountains at night, but you'd probably be travelling the mountains at night if you go the 77-26-95 route. Assuming you leave at 9 PM, you should hit the mountains around 2-2:30 am. It's an easy 45 minutes to an hour drive through the mountains.