Yes, this is possibly the worst way to play toons. The main point of this deck is to play off how the older toon monsters are worded, where they don't actually need Toon World/Kingdom on the field to attack directly (in this case, Blue-Eyes Toon Dragon and Toon Dark Magician Girl). You have the basic searchers, Bookmark and Tables, because if this deck is going to do anything, you will need all the searching you can get. Rollback, because why not, it's pretty much the only Toon spell you have access to without Toon World. Also Briefcase, which only requires a toon monster, for some reason.
So, even though you don't need Toon World to attack directly, you do need it for the summon right? Wrong! Because Red-Eyes Toon Dragon and Toon Dark Magician both ignore summoning conditions, so you need those as quickly as possible, hence Black Stone and Insight. Levianeer and BLS, because I needed to fill space, same with Chaos Space.
Does this deck work? Theoretically, yes, but since you have basically a clunky mess with no Extra Deck (you can do whatever you want with that, it's not like you'll ever get to it), and since you don't have Toon World, you don't have Comic Hand, Page Turn, Mimicat, or any other good toon support, you will probably lose by turn 4.
So why did I make this deck? Because I like finding weird loopholes in old cards. So if you play this deck good luck, you will need it.