Can't you make a perfect fox trap without a masterpiece knife?

[甜汤]

Can't you make a perfect fox trap without a masterpiece knife?

[PALU]

You can craft other things with tools of lower quality, so I assume it's possible for traps as well. Masterworks hide/fur requires a fine (normal kind of) knife, or a default quality broad knife, if I remember correctly, but better (and more appropriate) tools provide a higher bonus.