IMHO, a revolver is far safer than a semi-auto.
I agree, and have switched to carrying revolvers, and occasionally (very), a 629 in a high-ride holster. But it's a 3" and round butt so it's a bit easier than a 4" square (though maybe yours has a round butt if it's a newer production).
Unless you put that finer on the trigger, and stroke that long DA pull, you are not going to have a problem. The other things to be aware of are of course reloading, if you carry extra ammo. Some practice with a speedloader or a speed strip (they just recently came out with a .44 one after many years). Not as intuitive as an auto, but not impractical - you just need some practice.
The 4" 629 is a big gun. Toting it around all the time is annoying - same reason most folks don't conceal carry a Government Model even if they love them. a smaller snubbie in a K or J frame, or a Ruger model, are the more common choices.
Ammo for a .44 is also a consideration. .44mag may be a bit much for the urban streets, but .44 spcl, like a Hornady XTP or Speer Gold Dot, is an awesome defensive around, very similar to the .45 acp. in effectiveness. Similar weight bullets, velocities (edge to the .44 usually), and diameter. A truly great cartridge.
I will pick up some snap caps and start doing draw practice.. probably can find some vidoes on it on youtube for a revolver too..
Snap caps are not necessary for dry firing a S&W. Don't worry about that. But you are wise to bring that up - learning to get a nice long even trigger pull and keep the sights in perfect alignment until the hammer is down takes practice. I sincerely believe only copious amounts of dry firing can do that. Also, 45 minutes reading archived revolver information here will teach you 20 times what you will learn in 2 hours on youtube.
PS - there is a "search" feature on the tool bar of the forum, far right side above the last column. It will search just this forum and you can type things like:
"revolver reload(ing) technique"
"dry firing drills"
etc., etc., and you will find TONS of great discussions going back five or six years.