There is more than one way to skin this cat. One way is as I described earlier if the disposer is on its own circuit. Just disconnect the wires from the circuit breaker in the box. Another way is to is disconnect the wires in the switch, leaving the wires coming to the switch for the breaker panel attached to the switch and nipping the bare ends of the black and white wires going to the disposer off and capping them. That will render the wires going to the disposer in place but completely dead. You can just leave the switch alone as it will not do anything if inadvertently switched on. This would be the best way if the disposer is not on its own circuit because everything else on the circuit will still function. If you do this method, then you can connect the two wires together because the will be no electricity in them.
There is no reason to cap the bare copper wire because it is bare all the way through the Romex cable. What we are calling "caps" are actually called wire nuts and are use to connect 2 or more wires together in a junction box. They come in different sizes to fit the size and number of wires being connected, so you will need to determine the size wire you have. If enough Romex is showing, you can probable find this on the Romex cover. It would be something like these numbers. 14/3 or 12/3. This means size #14 wire and a ground (bare copper) or #12 wire with a bare ground. There are other wire sizes, they would not be in this wiring. #16 wire would be too small and #10 would be much heavier than necessary plus it is difficult to use that heavy of a wire in regular household circuits. Also more costly. If you can't see the number on the cover, then get a nut that will connect two #14 wires and a nut that will fit two #12 wires. Then use the one that works the best. (These are very inexpensive.) To use the nut, you just stick the two wires you are connecting into the nut and twist the nut tight. That all there is to it. The bare copper ground wire can just be shoved into the box as it is.
I realize this is rather a long dissertation, but in actual practice it is quite simple.