Dogtooth tengu thaumaturge and the weapon implement.

[Jak Kolchack]

Should dogtooth tengue use the beak attack as her weapon implement?
The rule reads, "You can choose only a one-handed weapon as an implement, which allows you to channel energies into your weapon as well as hold your other implements once you gain them." The beak is a one handed attack so as it's written it should work.
Thoughts.
Thanks.