There probably is no in-universe answer
Your question is asked from the perspective of a blacksmith in (a non-specific) world of D&D. It's easy to forget from our lofty perspective of meta-knowledge, but for the characters in the game, this information is basically impossible to know.
Remember that the creatures our exceptional adventurers might encounter range from the strongest demon lords, to unfathomable monsters from the Far Realms, to slumbering behemoths like the tarrasque. No individual will ever encounter all of these monsters in their lifetime. Moreover, the odds of anyone taking a sharpness tester along to figure out how an astral dreadnought's teeth compare to those of an aboleth seem... slim.
So honestly, anyone in-universe claiming they know what creature has the sharpest teeth is basically guaranteed to be exaggerating. At that point, they could probably pick anything sufficiently rare and known for having sharp teeth and claim that it's superlative. Nobody would really be able to prove them wrong.
There doesn't seem to be a meta answer, either
It's difficult to prove that there isn't an answer for 5th edition, but various searches on D&D Beyond yield no real results on the "sharpest" fangs. However, there are various adjectives that the descriptions apply to monster teeth. Perhaps these will suite your needs.
Really too many of these to mention, from goblinoids to dinosaurs to fiends. This probably isn't what you want.
The ghoul is described as having razor-sharp teeth.
Applied to the aeorian nullifier from Wildemount, and boy does it have a lot of them.
In at least one adventure, the death slaad is referred to with the same descriptor.
As hard as steel
The leucrotta has "bony ridges" that are described as "hard as steel," while still being sharp enough to "lacerate flesh".
Some intelligent creatures choose to sharpen their teeth. Whether this makes them sharper than those creatures with naturally sharp fangs is anyone's guess. These include hags, as well as various individual NPCs.