Do I just cap the wire ends, shove them back in the box ...
Before doing any work, check the light turns on OK, then go to the main panel and turn off that circuit. Go to the light and verify power is off by toggling the switch and checking the light remains off. After removing the light fixture, check the wiring is not live, use a non-contact tester if you have one but double check with a Cat-II voltmeter/tester. If in doubt wear electricians gloves and stand on an electricians fibreglass stepladder.
Before undoing any wire connections, write down which wires are connected where. Taking a photo can be useful. If necessary, mark multiple wires which are connected together at the same connection point - with tape a marker or something similar.
Keep the wires separate and use wirenuts (or similar approved insulating arrangement) to prevent the metal of the wires touching other wires or any nearby metal parts (box, coverplate etc)
You should only tie wires together if you are certain they were tied together before in connections for the working light.
Generally you don't see black connected to white (which would normally blow a fuse or trip a breaker) though there are exceptions.
It is always safe to completely isolate all unused wires. If you have only two wires (excluding any obvious ground wires) keep them separate regardless of color.
and stucco over?
No, the wiring needs to remain accessible in most jurisdictions. You could screw on a coverplate.
Bell blank covers are designed to provide weatherproof protection when a box is being used for junction. Blank covers have a flat face profile. Cover includes a gasket, mounting hardware and installation instruction.
These things seem to be well standardised, based on diameter (e.g. 4") but it may be prudent to measure the distance between screwholes in the box (hole centre to hole centre) before buying a coverplate.