As a retired Master watchmaker/gunsmith, I had to do a LOT of engraving on watches and jewelery, especially around Christmas.

The "engraving" is done with a pantograph device using a diamond or possibly carbide tip.
This literally scratches the design into the metal.
This is just deep enough to be easily visible on stainless, but too deep to remove if you ever want it off.

The key "watch out" is that the person doing the engraving isn't going to know anything at all about guns, so there's a good chance the engraving is NOT going to be properly aligned with the barrel and frame.
In other words, when you get it on the gun the engraving isn't going to be straight.
There's also going to be a good chance the edges of the side plate will be "dinked up" by the force needed to clamp the side plate in the machine.
Since the holding jig on these machines is set up for watches, bracelets, pens, and medallions there will likely be a problem with holding the odd-shaped side plate firmly or straight.
If the plate slips in the jig, the job will be botched, and there's no "fixing it".

My advice: Send the plate in to S&W's Performance Center and have them laser engrave it. They do laser engraving for very reasonable prices and it'll look a LOT better than the thin scratching as done by a jeweler's pantograph machine.