Here's some culturally-flavored axe designs for Ancardian homebrew shenanigans! While there are fantasy-stylings for each type associated with each culture, these are all meant to be practical and functional axes, with most of them being strongly influenced by one-handed and big battleaxes that existed in historical cultures. Of course, materials can vary wildly, but the ones depicted here are using the most ordinary material--Dwarven axes use steel of a Dwarven type, Orcish axes use a more Orcish-make of steel (which is actually harder and stronger but heavier), Kobolds, Gnoll tribes, and Sostunian humans typically use a very high-quality iron (with a lot of hard animal bone and antler for either handles or motif decor), etc. Quite a few of these are not strictly axes, but would effectively use the stats for a one or two-handed axe in 5e rules. I'm especially a fan of that Gnollish Axe-Club hybrid (if you were wondering, yes that beaut is directly based on a real historical club design).
Everything here that is called a "Hand Axe" or a "Throwing Axe" uses the statistics of the Handaxe, and pretty much all the others (except for the Northerner's Battleaxe, the Orcish Battleaxe, the Jotnar War Axe and the Sostunian War Axe, the Ogrish War Axe, the Faytun War Axe, and the more obviously-labeled Greataxes which use the Greataxe stats) use the ordinary Battleaxe stats. I've also almost got a sheet for the lighter types of swords done... there are a lot of them! Swords come in many shapes and sizes and I have no real favorite for a sword look as far as historical ones go!