I don't know of any writings about using the sword-cane other than standard fencing training. Sorry. There aren't even sword-and-scabbard fighting advice in any historical manuals I know. It's a bit weird.
I often tell stage combat students that they should know the historical, but be ready to invent new patterns of movement that suit their scene and character. I can justify this, even in a strictly authentic play, by pointing out that the manuals we have were not robot instructions, but rather advice to individual warriors, who will undoubtedly express it through their own interpretations. And if you can think of a cool move today, somebody who was using a sword in their daily defense and training had thought of that move, and probably used it.
That sounds convincing, and new innovations in swordplay and warfare did travel fast, but there is an equally compelling counter-argument when you look at the evidence. Men had been carrying walking sticks for centuries, and fought with them like regular fencing. Only in Bartitsu do we find Pierre Vigny who demonstrates that the stance with the hand above the head protects the hand which has no guard. Nobody had thought of that before, or if they did, they didn't write it down. Similarly, nobody thought of writing a novel until the 19th century.
So, we have no record of a manual on fighting with sword and scabbard, even though it seems a very obvious thing to do if that item existed in your culture. So you can believe that:
- Nobody thought of doing it until now, because of group-think or cultural weirdness, and somebody ought to write a book on it.
- Everybody thought of doing it, but it fails every time somebody tries it in a duel, so nobody wrote about it, and most were afraid to try.
- Some people did it and were good at it, but weren't the writing sort, or they did write it but the manuscript was lost or destroyed by accidents of history.
Okay, I lied about there being no instruction. Here's what Tony Wolf said in 2004: "I have one reference from Carl Thimm's fencing bibliography (1890s), stating that the Italian fashion of using the sword cane involved holding the cane in the left hand as a parrying implement and the sword in the right hand, to thrust." So it's hardly a manual.
There are plenty of writers who mention it, usually along the lines of Mr. Allanson-Winn: "The sword-stick is an instrument I thoroughly detest and abominate, and could not possibly advocate the use of in any circumstances whatever..." Read his further comments in this nice article from Out of This Century: The Victorian Gentleman’s Self-Defense Toolkit. It boils down to... Q: How do I fight with a sword-stick? A: Don't.
Is Cane-Sword Fighting Part of Bartitsu?
The strict answer is no. We have no evidence of that.
BUT...
If we consider that historical recreation of medieval and renaissance martial arts and swordplay were happening in the Bartitsu Club, and some of the upper crust members must have had sword-canes, if only as a curiosity (as today), could they have tried to combine smallsword with Vigny's cane? I am doubtless they did. But they were never ready to write down their experiments for one reason or another. That's my opinion on the matter.
And if anyone wants to experiment with me who has smallsword and cane experience, let's try it!