If it does download, you're right - Settings > General > iPhone Storage. If there's an iOS download present you can delete it.
Personally, I don't get this fear-of-updates, but I've been beta testing software since 1994 - I'm one of those weird people who say, "Bugs come and find me!" I'd rather have new features, bug and security fixes, and potentially improved performance, and am willing to take risks to get them.
I don't subscribe to the conspiracy theory that Apple wants to cripple old gear so I'll buy new. Over the years I've kept some pretty old Apple hardware running by updating the OS. The best example is my old 2008 iMac, which is the Mac I "retired" due to declining performance when I bought the late 2013 iMac I'm using to write this post. Alas, that 2008's HDD is sick now (and I'm not motivated to replace it), but some of the performance problems it was having back in 2013 cleared up with subsequent OS X releases - my youngest still uses it for coding when he comes to visit. That iMac came with Leopard (10.5), and I've taken it to the top of El Capitan (10.11.6), which as far as Apple will let me go.
Certainly, there are times when putting new demands on old hardware will hurt performance, but my experience with Apple generally does not bear that up. The late 2013 iMac upon which I type this is working as well or better on the current Catalina beta (macOS 10.15) as it did, brand new, with Mavericks (OS X 10.9). My first-generation iPad Pro, which came with iOS 9.1, is running the iOS 13.1 beta without a hiccup.
Have I had some poor experiences over the years? Yeah, but when balanced against what I've gained by upgrading, I'm more than willing to keep taking the risk.