I'm not sure what carbon cloth is but I'm assuming it's some kind of heat resistant product to protect the surrounding area.

They do sell push-on fittings that require no soldering. They're more expensive than regular fittings but if you less than confident in your skills might well be worth the few extra dollars.

I don't think it's a problem to sweat it off (I'd use the little fireproof blanket thing you can get in the plumbing section), but I'm wondering more about how easy it is to clean the pipe afterward and sweat something else onto it. Wouldn't that be a pain if there's any solder at all left on the pipe?

"I'm wondering more about how easy it is to clean the pipe afterward and sweat something else onto it."
Reheat the pipe to where the solder residue is molten, then quickly use steel wool to clean the end of the pipe. It's a two-hand job as you don't want to take the time to lay your torch aside before steel-wooling the pipe end.

Here are a couple of things I have done (or seen done) in similar situations:

-put a piece of sheet metal between the joint and the wall, notching the sheet metal for the pipe if need be.

-spray your water ahead of time to wet the wall near the work area.

-once I had a plumber do some work, and he had some spray-on fire-resistant stuff that was viscous like jelly.

-Here is a suggestion to minimize the heat you will have to use there. I find that if access is tight, I have to spend a longer time with the torch on the joint to give me the time to get the solder to the joint. Therefore, once or twice I have used pre-soldered fittings in close quarters. I think I still used regular solder, but it was nice to know there was some already in there, so I did not tarry with the torch.
Since you are, I think, trying to solder in a valve, I would use something like this, namely, a pre-soldered coupler. Then use a stop valve with pipe thread:
{{!gwi}}

Here is a link that might be useful: pre-soldered fittings

Thank you all so very much. I don't want to start any fire so I want to take all precautions necessary. The carbon cloth is the fire resistant material I will use.
I have also heard of material to put on the wall that is fire resistant. Does any one know of any brands and Is one brand as good as another? And yes, this is very tight quarters so I was thinking of using those push on fittings. Shark bite and gator bite? are two of them. Are there any others and is one better than another?

First make sure the water is turned off and the line drained.

Next put on a pair of leather work gloves and have a fairly large cotton rag handy (an old Tee shirt is perfect).

If your right handed hold your torch in your left hand as near the wall as you can with the torch tip and flame pointing out towards the valve and away from the wall and have a pair of channel locks in your right hand.

Heat the valve and try turning it with the plyers, as soon as it will turn give if a twist and pull outward and the valve will slide off the pipe. Lay the valve aside, but don't forget, it is hot, you should have some corrugated cardboard or a bucket to drop it in so it won't burn the cabinet or floor covering.

now grab the cotton rag in your right hand and reheat the end of the pipe till the remaining solder melts, remove the heat and grab the pipe with the cotton rag and pull towards the end of the pipe, that should remove the excess solder leaving just a light film on the copper as if its silver plated. If not, repeat the heating and wiping a second time.

Now set all that aside and let the pipe cool then take a1-1/2" wide strip of emery paper about 6" or 8" long and loop it over the end of the pipe and pull the emery back & forth like a shoe shine rag from two or three directions to insure the excess solder is cleaned off.

Now get a compression type angle stop valve, Slip the compression nut on the pipe, then slide the compressing ferrule on the pipe. Now slip the new valve on the pipe as far as it will go, then slide the compression nut ahead to the valve and tighten the nut. You need two tools to properly tighten the nut, once wrench to hold the valve steady while you tighten the nut with a second wrench.

Note.... the fixture stub out is normally 1/2" copper pipe.
Compression fittings are primarily used on copper tubing so they are generally listed by "tube size". Pipe is measure by the OD while tube is measure by the ID so when selecting a new compression type angle stop look for one that says 1/2" copper pipe or 5/8" tubing, they are both the same size and will fit your stubout.

Thanks lazypup,
your directions were perfect. I shouldn't run into any problems with this guidance. Thanks again.