A way to compensate for a smaller blade is having it made with “rare metal” or with “magic” whichever may fit your story better.
I own my own cane sword as well, the blade itself was dull from before I bought it, but it’s more like a dagger.
As far as cane design, if you taper it down to a strong point it’ll be less suspicious. If you have the handle lock a pressure turn you can make it look more like a 2×4 that’s been quickly sanded and turned into a cane, it won’t be too suspicious but not completely hidden.
If we’re stepping outside the range of what’s possible, and into straight up fantasy weapons, I still adore Bloodborne’s Threaded Cane. It’s not technically a sword, since it goes from being a cane to a serrated whip, but still.