Posigan,
1. You're probably noticing a lot of carbon staining on the stainless steel that will be very difficult to get off with regular solvent.
You need "Lead Away" cloths for that. These remove carbon fouling and lead deposits very nicely. Just do NOT use them on blued guns!
As for the sideplate, you really only need to remove and clean under there every couple thousand rounds. The beauty of a revolver action is that it is almost totally sealed against carbon fouling and other associated dirt.
I would not shoot cleaner in there. The only thing you're going to do is move existing dirt around, and likely remove all traces of lubrication.
Taking the sideplate off, though, isn't all that hard, and you don't need to disassemble the action to clean in there with the side plate off.
Simply remove the grips, then remove the screws in the sideplate one at a time (keep them in order!).
Then, hold the gun in your off hand, topstrap and sights toward your thumb. With your thumb, gently restrain the sideplate, but don't press down on it.
Then, with a wooden hammer handle, nylon or rawhide mallet, or lead bar, sharply and squarely rap the middle of the grip frame (the sides, not the front or rear of the grip).
Several whacks may be necessary, but the sideplate will "pop up" and can then be removed. Make sure you do this over a padded are or carpeted floor! If you drop the sideplate on concrete, you can warp it or really bugger it up.
Also, NEVER try to pry the sideplate off. It will warp.
There is one loose piece in there that you need to watch for, and you really should havea disassembly diagram for that.
With the sideplate off, you can blow it out with Gunscrubber or some other cleaner, and then let it dry. Then, apply oil and/or grease so that you get a nice covering over everything.
To really properly grease the action (I prefer grease, as it doesn't migrate out of the action) you should disassemble the gun.
When you're putting the side plate back on, be sure to get the little "hook" at the top of the plate under the face of the frame. If you don't, you'll really screw things up.
When you get the plate aligned, tap it gently into place with a non-marring mallet (I usually use a piece of dowel rod that I've drilled out and poured lead into the end).
Then reinstall the screws. Don't tighten them down one at a time. Get them started, and snug them up in sucession just as if you are putting the wheel back on a car. That's extra assurance that you're not going to warp the sideplate.
2. An action job can GREATLY improve the trigger pull.
There are several stages of action jobs.
A) Springs only. In this, the mainspring and the rebound slide spring are replaced. Both have an effect on the felt trigger pull. Once you get to know the interior of your Smith a little better, you can easily do this yourself.
B) Action smoothing. This is more intensive, and more expensive, and should be done by a qualified smith. In this the gun is completely disassembled, and all of the internal parts polished and smoothed.
Done in conjunction with A, the improvement in trigger pull weight and feel can be absolutely unbelievable.
I've reached the point where I'm now doing both A and B. I did a friend's Smith 36 the other month. It started out with a trigger that was crunchy, nasty, and heavy.
I replaced the springs, and it made a big improvement, but it was still crunchy. When I did the smoothing job, it turned a nasty action into a very very good action.
As someone mentioned, changes in the springs can cause ignition problems. If you have this done, you should always fire the gun extensively with your chosen protection ammo BEFORE you rely on it.
I've never had a gun fail to fire reliably (I've now done probably 30 for myself and my friends) after just replacing the springs with a Wolfe springset.
Reliability normally becomes a problem when you start snipping coils off springs, start messing with the strain screw location, etc.
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Beware the man with the S&W .357 Mag.
Chances are he knows how to use it.