It's safe. It's worthwhile. It's a persistent myth that older Macs slow down with newer OSs.
I updated my 2012 Mac Mini to Mojave shortly after it's release, with no trouble. Note (see below) I had already replaced the Fusion Drive. (see below)
You certainly should update. The NEXT time you probably will not get a choice, as your hardware will "age out" and will be unsupported on MacOS "N...."
You will get warnings about 32-bit apps and control panels. You can ignore them. They WON'T work On MacOS "N...."
If anything, it should be faster. MacOS is not a Microsoft OS!
Every new update gets these stories about "slow", when usually it is nothing more than Spotlight rebuilding, etc. which is transitory.
My biggest concern about your Fusion Drive is that the hard drive is almost certainly having a near-death experience at this point. Replace it with a flash drive. It will make a HUGE improvement in speed. Not sure if your iMac requires cutting a rubber seal or if the front glass can be removed with magnets.