Here's another video of the blade action in, well... action.
Stick with acrylic sheets for the blade, you can find them at most home improvement/craft stores, and check with your convention if you really want to make the sword spring loaded. Many have rules against things like that, would be a shame to go through the trouble of making a functioning version and then not be allowed to carry it due to neglecting to check policy ahead of time.
At 57 seconds you can see that the tip segment of the blade slides inside of the base segment. What this means is that you're going to be making a two part slide. The base blade segment can be made to move like a standard out the front switch blade, however the structure of the base would need to be hollow so the tip segment can slide out. The same concept as the toy lightsabers that can be swung open.
To keep the tip from sliding back inside the base you can cut channels inside the base segments and add pegs to the sides of the tip segment so that it slides into an offset in the channel and locks. Another option would be to sand in a taper to the inside of your base segment so that it would 'lock' through friction. Still another option would be to incorporate a second spring that would push out and hold the tip section in the extended position; problem with this is that you have to also incorporate another locking mechanism to keep the tip segment from always popping out.
Only problem you'll have is that there will be a noticeable difference in the thickness of the blade.
The collapsible cane idea is another option, the only thing I'd worry about here is how the blade would orient its self upon release. With the cylindrical cane you don't have to worry about how it pulls the next segment, the blade needs to set a certain way so that the edges line up.