Welcome to the Armed United States of America. I recall when I first got into detecting and would find bullets how I marveled at it all. It is exciting to find them at first, especially if you have little experience with firearms. I wouldn't trouble myself to fire the thing in a gun, though, as it is likely a pointless effort - it will most likely only sit there at the hammers fall. If it was me, I'd just toss it in the "finds box" and impress your friends with it now and then.
Sounds like what I'm saying flies in the face of good reason, right? Well, loaded cartridges are inherently safe, in and of themselves, contrary to what many will have you believe. Their intended purpose, in fact, is to do absolutely nothing until fired in a gun, regardless of the sort of handling they receive prior.
Did you see the movie, "The Lord of War?" In the movie they showed Russian 7.62x39 rounds bulk packed in a big box, loose. Then they were shipped willy-nilly, knocked around and spilled on the ground - generally mistreated all over the war-torn world. For all of that, they arrived intact, sadly, to wreak their havoc, no matter how badly they may have been mistreated in transit.
Something else to keep in mind, is that the component parts of modern ammunition break down readily when exposed to the elements, so it's highly unlikely the round you found under the wood chips remains viable. Only some military ammo of fairly recent vintage poses much of a viability threat, as the military normally lacquer seals their ammo against moisture intrusion.
But, even if that .357 Mag round was viable, it might comfort you to know that I have what, to some, would be a shocking amount of live ammo stored in my shop - and none of it has gone off by itself. Ever. Ditto the handloads that I have created myself.
(Now, if you insist on hitting it with a nail and hammer to test out what I'm saying, well then, you are on your own and I disclaim any liability in such an event!)
In fact, just for the sake of argument, I set a genuinely "live" .35 Remington cartridge of recent manufacture on my desk as I typed this. I picked it up from time to time, rolled it around and even shook it a few times. GASP! Guess what? Nothing.
My first detector-found cartridge was an unfired military 7.62X51 NATO round under an old tree. Dead as a stone and still in my box. Since then, Ive found fired and unfired ones, live and dead ones, old ones and new ones, modern and vintage ones. I recently turned up a bunch of .32 WRF's at an old house site and a handful of live .22's laying on the ground at another (It is fair to tell that the local "projects" is next door to the 2nd house and I have found other places to hunt!)
All of these "bullets" lie at rest in my "finds box," none the worse for wear. The same can be said for me, for having them there. You just have to understand the risks youre dealing with. I also don't think we should remove swingsets and merry-go-rounds from playgrounds, but that is another issue...
While I have never found an entire gun, others have and I have found gun parts. Some make a case for gun control out of such stuff, others like me are more in favor of idiot control.
But the fact remains that small arms ammunition in all its forms is a part of the detecting experience. Watches too. You have gotta love it!