Just to be clear, the LAS-DEN-NRT legs will presumably be on UA since NH doesn't serve DEN. Note also that there is no exit immigration control when departing USA.
All airside areas are connected at LAS, so it is possible to get from any WN gate to any UA gate airside. The only issue would be if OP is checking bags, as WN does ground handling in T1 and UA does ground handling in T3, and it is not possible to get between the landside areas of T1 and T3 quickly (there is a free shuttle bus which is supposed to run every 15 minutes, but I've read reports that it runs irregularly).