It's probably a bit late for me to put this up, but from the point of view of a long time weapons checker at a major UK LRP system, I've seen scabbards made for katana made from a number of different things. I've seen them made of plastic plumbing pipe and wrapped in leather or vinyl to match the handle, and made straight out of leather stitched into a tube, and made of Plastazote (the same material the weapons themselves are made of) and either painted or covered to match the weapon.
Plumbing Pipe Method
The plumbing pipe method is normally done by heating the tube and using something to flatten it from circular section to an oval that better fits the profile of the blade - a pair of G-clamps, a pair of 2x4s and a heatgun would give you an even cross section. The problem that you then have is the curve of the blade. The best way to deal with this is to draw around the blade of your weapon for a template, and take the flattened tube, and keeping one end of the tube held in place, apply an even heat up the length of the tube, and curve it to match the template.
For straight blades, the plastazote and leather methods are pretty straightforward - take enough leather or plastazote to wrap around your blade tightly enough not to just fall out but loosely enough to draw, and glue/stitch the ends into a tube. Add decorations and endcaps, and you're pretty much there.
Curved leather ones become slightly more difficult as you'll need to have two pieces - one for either flat side of the blade - that you stitch together into a 3D curve so that it doesn't just collapse flat when the blade is drawn out, making it difficult to sheathe.
Plastazote Method details
My recommendation would be to use more Plastazote to make the scabbards. Make a template of your blade by drawing around it onto a piece of paper or card, and measure the thickness of the blade.
Place your template on a piece of Plastazote long enough to fit it with room to spare around the outside of the template, and draw around it onto the Plastazote.
Mark out from the line you've just drawn by 2 mm plus the thickness of your Plastazote. So if you're using 8 mm Plastazote, mark out 10 mm around that line.
Katana scabards are normally straight at the end - it doesn't curve to match the tip - so extend the 10 mm line so it runs parallel to the top edge of the blade, then cut along that 10 mm line, so you should end up with something like this:
Apologies for my crap drawings.
The dotted yellow line shows the line you drew around the template.
Make a duplicate of this piece, so you have two matching pieces.
Next cut two strips of Plastazote as long as the longest edge on the pieces you have just cut, and as wide as the thickness of the blade plus 2 mm - so again, if the blade is 18 mm thick, cut the strips 20 mm wide.
Glue these to the two long edges of your first piece, then glue the second piece on top of this, as shown below:
You should end up with something that has a cross section like this:
Hopefully, if my instructions have been clear, and the measurements have worked, you should end up with a square section tube that your katana can slide in and out of tightly but easily.
Cut an endcap to glue onto the bottom end of the scabbard.
Chamfer (round the corners) and sand them so it has a less rectangular and more oval outside cross-section:
Add decorations and paint the outside only to match your weapon. If you paint the inside, the weapon may bind to the latex. I recommend a gentle wipe-down of the blade with silicone spray (don't spray the weapon, spray a cloth, and wipe the blade with the cloth) to stop it from trying to bind in the scabbard anyway.