I swapped my rims tonight, and took the opportunity to take some photos while I went.
This is for a GL Interstate, very similar to the CX.
1. Remove luggage and rear seat or trunk. There are two 10 mm bolts to be removed from inside the rear fender area, accessable only with the seat off.
Unlock your rear helmet/seat locks with the key and rotate the handles forward. This pic shows the handles almost to the release position.

Push them both forward, and the seat will release. Here is a pic of the mechanisms.

These are the bolts to remove, each side, 10 mm.

Removing these allows the back of the rear fender to pivot up and out of the way, giving clearance for the tire to be removed. Rob's site mentions losening rear drive bolts, this is not necessary if you do this, but recommended for final installation for axle alignment.
Here I am lifting the fender. Note for the interstate, there is a cross bracket that goes from left to right that needs to be removed to allow the fender to pivot

That done, now we get to the wheel. You need to remove the brake actuator nut, and the brake holding arm (not technical terms, so sue me lol)

Note 14 mm

There should be a cotter pin on this, which you need to remove, and preferably replace. Don't ride without it (put a safety pin in or something if you have to). Mine was 13 mm. Wierd size, may not be original.
Loosen the pinch bolt on the left side of the swing arm. No need to take it all the way out. 12mm

Remove nut from right side. 19mm

Drift out the axle from right side to left. Not location and orientation of spacer on the left side, between axle and hub.


you should now be able to pull, wriggle the axle free from the left side.

Note that the brake drum will now be free as well, a great time to check the condition of the shoes.

Here is the date code for my new tires. 3408 thirty fourth week of 2008. Fairly fresh tires. When getting new skins, check your code, if they are more than 2 years old, don't accept them.

You now will be able to wriggle out your rear tire/rim, lifting the fender to allow clearance.
When reinstalling, grease liberally the splines. But only on the wheel, not the hub. If you do the hub, you will get grease on the tire when you put the rim back in place. Trust me on this one lol. I did it wrong as the picture states. I greased both, thinking there can't be enough. Now I have to degrease my tire before I ride.

Reinstallation is essentially a reversal of the above. I will note however, put the engine in gear. You will know for sure when the wheel and the hub splines engage. Don't forget your cotter pin on the brake holding arm.
There were some good comments on the thread which I will paraphrase for you here:
Len in PA added:
I would only add that loosening and tightening the final drive nuts assures proper axle alignment.
gmcwayne
I did not have to move the fender out of the way to clear the wheel, but I did have to deflate the tire a bit to clear the final drive.
Others stated the same. I think doing the fender lift is just as easy or easier, but dance with the one who brung ya.
I was asked about silencer removal
On this bike I had an aftermarket muffler on, larger diameter, So it did have to come off. Note it's there when I am doing the pinch bolt.
On the other bike (where these rims came from) no removal was necessary, your mileage may vary.
Cheers