No, you cannot take out those screws one at a time with the gun otherwise assembled. Well, you can but parts inside will probably shift. I've never heard of washers for those three screws. Blue loctite is your friend. Many people use it on the various screws of the single actions. Just be sure to clean off any grease or oil on the threads before using the loctite.
As for disassembling the gun, the SAA is quite easy to take apart. I think there are articles and probably You-tube videos online that explain it. I even wrote instructions a while back and have probably posted them on this site but not sure where, so I will post them again here. Note that these instructions are for a Colt-style percussion pistol, but as the last paragraph states, it is the same for the SAA guns. Good luck.
On a Colt cap and ball pistol, first loosen or remove the wedge (right to left unless it is a Walker). It doesn't need to come all the way out the left side (you may have to remove the wedge screw for the wedge to come completely free), just make sure it is hanging loose on the left side so it is no longer holding the barrel to the cylinder pin (also called the arbor).
If the gun is an Uberti Richards-Mason or Type II Richards conversion, or a '71-72 Opentop, the wedge screw has a flat on one side of the screw head. Turn the screw counterclockwise until the flat is facing downward towards the wedge, then the wedge can be removed from the gun.
Pull the barrel forward away from the frame. If it is really hard to remove (be sure the wedge is removed), you can help it by using the rammer to push against the cylinder in between the chamber holes.
If the gun is an Opentop or Conversion without a rammer and the barrel is hard to remove (be sure you removed the wedge!), you can take a wooden dowel that is small enough to fit inside the bore and long enough to stick out of the muzzle an inch or two when inserted all the way into the barrel and cylinder so the end of it is against the recoil shield. Then while gripping the barrel at the muzzle with one hand, use a plastic or wooden mallet of some sort to tap against the protruding end of the dowel, and this will push the frame away from the barrel. Be sure the back end of the gun (frame) is in your lap or over a padded spot so it doesn't fall against anything hard or rough when it comes loose from the barrel.
Put the pistol on half-cock, which will drop the bolt head into the frame and unlock the cylinder. Now you can pull the cylinder forward off of the cylinder pin without leaving a scratch from the bolt.
Pull the hammer back to full cock and then let it back forward. On some guns, when the cylinder has been removed the hand will stick forward in its frame slot enough to bind against the frame and prevent you from being able to pull the hammer to full cock. In this case, push the hand back into the frame with a screwdriver tip, or a pencil, or anything else, while you pull the hammer back to full cock.
Remove the backstrap by removing the two screws at the top of the backstrap, on either side of the hammer, plus the screw in the butt of the grip. When you pull the backstrap away from the gun, the one-piece grip will come off with it.
Remove the triggerguard by first loosening the large screw that holds the mainspring in place, which will take tension off the spring, and then removing the three screws in the bottom that attach the triggerguard to the frame.
Keep track of where the gripframe screws go. The two at the top of the backstrap and the two at the rear of the triggerguard are all the same, but the one at the front of the triggerguard will be different (smaller head) and the one in the butt of the gripframe may or may not also be different.
After removing the triggerguard you will see the action parts inside the frame. There is one screw inside, which holds the two-pronged trigger-bolt spring in place. Before removing this screw and the spring, note how the long leg of the spring pushes against a ledge on the trigger. When you reassamble the gun, be sure the end of the spring is against this ledge the same way. It is fairly easy for the end of the spring to get underneath the ledge instead of on top of it (when the frame is viewed upside down).
Remove the screw from the side of the frame that holds the trigger in place and remove the trigger.
Remove the screw from the side of the frame that holds the bolt (cylinder lock) in place and remove the bolt. You might have to slide a small screwdriver underneath the forward end of the bolt and pry it away from the frame in order to get a grip on it to remove it (the legs of the bolt are still squeezed between the hammer and the frame).
Remove the screw from the side of the frame that holds the hammer in place. The hammer can then be pulled downward out of the frame, and the hand will come out with it.
Reassemble in reverse order. The hand must be attached to the hammer, and it can be a little tricky to get it started up into the hand channel. You might need to compress the small leaf spring on the back of the hand to get the hand to fit into its channel in the frame.
Installing the bolt can also be made easier by pushing the legs of the bolt into place with the hammer pulled back, then hold them in place as you let the hammer back forward.
When installing the backstrap and grip, it is usually best to alternate between the two top screws and the one in the butt, screwing each in a little at a time.
Hope that helps.
p.s. with the exception of pulling off the barrel, the above steps would be the same for an SAA, except the modern reproductions mostly have a coil handspring and plunger and setscrew in the frame instead of the leaf spring on the hand, and these parts must be removed before the hammer and hand are pulled out of the frame or they might fall out into the hand channel and be lost. And some of the Pietta SAA clones do not have a setscrew behind the coil hand spring and plunger, so when you take off the backstrap, the coil hand spring and plunger can fall out so be careful.