It’s my impression that a substantially different look starts with a custom layout. I’ve never tried creating one, but a did read through @Brian_Radspinner’s comprehensive tutorial at one point, and my impression that this is not for the faint of heart, but does not have to be overwhelming. It does require some basic TW skills and at least intermediate HTML/CSS knowledge.
But what does your “doesn’t look or feel like a wiki at all?” mean? @Jeremyruston’s commercial site, https://www.intertwingledinnovations.com/ is not a wiki, but except for a beautiful animation on load, looks a lot like a read-only TiddlyWiki… quite intentionally, I’m sure. @Christian_Byron’s HexMap and my Periodic Table show tiddlers with unconventional layout and interactivity, but within an otherwise normal looking TW. @Charlie_Veniot’s Basic Anywhere Machine has a custom layout designed like a WIMP interface. So there’s a lot you could do if you set your mind to it. But what do you actually want to do?