What you want from your glass sword is aesthetics; it doesn't seem essential that it be technically a form of glass. What I propose is actually a crystal.
Sapphire is the pure crystalline form of (otherwise very common) aluminium oxide. It is extremely hard -- much harder than steel, and nearly as hard as diamond -- and quite tough. It isn't as tough as steel, but similar to cast iron, and very much tougher than glass. It is also much more resistant to high temperatures than steel, so at white heat it is actually tougher than steel. And it is -- or can be made -- water clear, far more transparent than ordinary window glass. It is about half the density of steel: light, but still much denser than glass, plastics, or light alloys, so perhaps making for a sword that it fairly lightweight, but has some heft for powerful blows. Alternatively, the lower density could be "spent" on making the blade thicker and wider, for greater strength.
It's no surprise that natural sapphire is a prized gemstone, but in the mid-twentieth century, we learned how to make synthetic sapphire fairly economically. By the end of the twentieth century the technology had progressed to the point where we could make huge synthetic sapphires -- potentially sword sized, perhaps even bigger.
Although this technology was developed well after your period, the basic tool required -- the hydrogen blowtorch -- did exist in the nineteenth century, and it is quite plausible that in an alternative timeline, synthetic sapphire may have been discovered far earlier.
Why would someone want a sapphire sword? One or more of the following reasons might apply:
- Use at very high temperatures (how the wielder survives is an exercise left to you!);
- Superior corrosion resistance in many environments (but not in alkalis, which damage it rapidly);
- Not affected by magnetic fields or electric currents;
- Superior hardness and extreme sharp edges (but the very devil to re-sharpen if you damage the edge);
- Coolness for a social elite: the hoi polloi can have their common steel pig-stickers; us gentry use only the purest crystal swords.