risky can have a few definitions
like, risky because of malware? then you just need to not be stupid as to where you download them. risky because of crashing your system? then you need to read forums to see if others with your OS experience higher crash rates.
make sure you check RAM and CPU consumption to make sure you aren't running too many things at once.
Generally speaking Linux can be faster than windows at an OS level, but this is rarely a distinguishing feature between the two. In my experience, only the tech world seems to run Linux(there are exceptions), so for your everyday consumer, Windows is the norm. So most software for average consumers is specifically targeted at Windows users. Note PC games, Windows support will come out first for indie games, then Mac, then Linux. So unless the people who coded the emulator started with the Mac or Linux version first, the Windows version should be the most stable
What you need to do is have Resource Monitor open when you run it. Make for goddamn sure it does auto run on startup. If it gives you problems, uninstall it. no problems should persist after a clean reboot unless it's malware.
If you're running a trusted emulator than the emulator alone shouldn't cause any harm to your system. If you're running a random emulator that has very little info or support, then that's a bit more worrisome and those should be avoided. This thread https://www.speedrun.com/Speedrunning/thread/19h43 has a list of emulators that are commonly used and are considered valid for runs. For many newer systems (PS2, Wii, etc) the emulators may not be valid for runs but there are trusted emulators for them like Dolphin.
If your computer isn't the greatest you might notice some performance issues like slowdowns when running the emulator but that's not causing any harm or anything, it just means your computer isn't strong enough to run the emulator alongside any other programs/windows you have open.
ZSNES seems to be banned for speedrunning but Project64 v1.7 is good. (no mention of 1.6, i suggest upgrading) Look to see which SNES emus are commonly used for the games you want to run
PJ64 1.6 and 1.7 are usually legal for speedruns (ask game mods just in case), but PJ64 2.x tends to run faster than real hardware so those are usually banned.
For SNES, ZSNES and models of SNES9x 1.43 and below are usually banned for inaccuracies so a model of SNES9x above 1.43 is your best bet for those games.
ROM hacks can be run on emulator, and usually are, however for older consoles they can be run on real hardware using a flashcart like an Everdrive.
When in doubt, ask the mods what emulation rules they have in regards to banned emus/emu versions.
I'm still not sure what you mean by safe.
An emulator alone, as long as it's a trusted one (see the thread I linked a few posts ago) and not a random package of code distributed by an unknown website, will not harm your computer while you use it. If your computer isn't that good, you'll see performance issues but that's just caused by old/weak hardware. It's not ruining your computer or anything.
The only way you'll get something harmful that will harm your computer is if you click on random links while downloading anything. Then you run the risk of getting malware, viruses, etc. As with downloading anything online, be careful of what you click.
For what it's worth, yes, ZSNES and PJ64 are trusted emulators (allowed for runs is a different story like already mentioned). But as always, safe internet browsing habits go a long way with downloading anything from the web.
If you're asking for links to download emulators or something, you won't find those here as these forums aren't the place for distributing those kind of things.