now, I am not entirely sure if it's the same way everywhere, but at least in the con's I've gone to, carrying metal swords is forbidden, or, if allowed, it is forbidden to unsheathe metal swords, weather they have edge or not.
Also, let's face it, a true sword, even a prop metal one is not exactly cheap
Wood Sheets [1 of (5 to 7)mm and 2 or 3 of (7 - 10)mm] (I recommend you read the rest to explain why the sizes and amounts)
--- here I am using basswood, for all of the sword, first, because it's a soft and easy wood to work/carve, and secondly, because I don't have power-tools to work with harder woods, but if you do, feel free to use them, and use harder woods.
Cutter (like a snap-off blade) / wood-saw or other wood cutting tool
Paint / spray paint (silver/metal, gold/bronze, and black/brown)
flat shoelaces (not the rounded ones) / seam-cloth (sorry, don't know the actual name)
Step 1: Step 1 - Study your swords
Most important thing in making replicas is to study the originals,
so, yeah, there are plenty of pages around where you can find the makings of a katana (or other swords in general, actually). And, most importantly, it's parts
image isn't mine, there are quite a bunch of images in google, and names, and stuff
se sure to also considered exactly how much detail you want to add