Hi Sam, your post made me laugh - in a good way :) (Based on your post, I'll presume? you are a man. Some women have a nickname - Sam.)
Since you have already traveled about in other big cities, touring Naples should be okay. Practice awareness and keep a big city attitude. If wearing a money belt (tight & secured under your clothing) makes you feel better, then go for it. Make sure the clips are secured.
I've been to Sicily but not Naples. On that trip, I carried a (medium) leather cross body purse - zip closure and a good safety strap. No issues. My friend carried a purse and had no issues either.
In the last couple of years, I've discovered Kipling - which has a ton of bags/totes/luggage to choose from to meet a person's travel needs. Most are very lightweight and can hold a ton - your daily stuff and purchases along the way - without worrying about carrying too many little bags. They have unisex bags.
I saw many men carry (small, messenger type) bags in Sicily, Northern Italy and Rome.
[side note:] On my first trip to Rome, I used a money belt, pinned it for extra security. But, I began using a mini Hedgren cross body to store some extra Euro, card and Passport.) It is my preference to carry my PP. Varies for everyone. I secured the bag under my jacket/coat.
I'm not a backpack person, but for those who may be, I thought this unisex bag https://tjmaxx.tjx.com/store/jump/product/Nylon-Backpack-With-Rfid-Protection/1000467651?colorId=NS1003537&pos=1:52&Ntt=backpack was nice and a good idea. Of course, secure the zippers.
The zippered compartment for your valuables are facing inside against your back. This is the same material as my mini Hedgren I often reference. It's easily concealed under a jacket or coat. I have been using a Kipling zipped tote for my dailies.
[adding:] Oh yeah, my friend and I did ride a couple of buses in Sicily. They do get crowded. We just went to the back of the bus and stood against the "wall of the bus" facing the travelers. As someone mentioned, just be more careful on buses/trains anywhere, really.
Edited to correct a sentence that was confusing. lol.