Mouthpick weapons already exist, they're in Lords of Madness (Which actually reminds me to make a note about those...). Not to mention dog-like creatures using swords is a big thing in fiction:
Spoiler
And that's not even all of them. Repede from Tales of Vesperia, Hessian Lobo from Grand Order, Cracklefang from World of Warcraft. Dogs with blades is a common enough thing.
TBH, I'm actually MORE surprised that you've never heard of the concept before.