You don't need root to use a standard icon app. But you will find that won't change system app icons or elements. So it's limited in it's scope. Rooting may affect your warranty if Verizon found out about it. The logical extension of that is to revert the root before making a warranty claim. There shouldn't be any permanent evidence of rooting provided that you don't increment the Knox flag. Note that some root methods will increment the Knox flag and some e.g. "Towel root" don't.
For the "theming" that you want to do, it sounds like you will need root. And you should be able to root without incrementing Knox. Note that Verizon is more restrictive than most carriers and a custom recovery, kernel or bootloader will also trip Knox. You can probably emulate a custom recovery through a program called Safestrap though.
Nor it is assured that incrementing Knox will void your warranty. Samsung will try to disavow a warranty if you do, but they are on shaky legal ground there. And most warranty claims are handled through carriers, not directly with Samsung. And most carriers do not care about the Knox status, although I don't know Verizon's position on that.
It doesn't sound like you read many threads in the forum or did a search before posting though or you'd already know much of this. That's an unfortunate habit and you should consider doing a search before posting. There is a wealth of information in existing threads that often answers your questions immediately. And in any case puts you in a more informed position to ask questions and you understand your phone better in the end.