I’m not convinced an umbrella would be a good place to hide a blade, given the mechanical complexities would mean there were so many more things that could go wrong. It’s one thing to have an umbrella, but what happens when the umbrella mechanisms start breaking?
That said, umbrella swords do actually exist, and you can buy cheap knockoffs for a couple hundred dollars, online. There’s also umbrellas with various sword hilts because… it’s the internet, so of course there are. Just like the sword canes that masquerade as revolvers, because when you’re trying to conceal a sword, your best choice is as a different weapon that people are more likely to be worried about. They’d never suspect you’d actually stab them with a gun, that’s ridiculous.
Anyway, I actually have a cheap sword cane around here somewhere. Now, even at their best, they wouldn’t be able to keep up against someone using a sword intended for heavy combat. But, if your character can carry a cane without coming under a lot of scrutiny, and isn’t trying to take it through a metal detector, it might just be their best option.
I’m also going to post this link. It’s to an ask we got a while ago about fighting with umbrellas.