As for the first topic of animals’ natural weapons outside fights, I think you have latitude as a GM to include both narrative and mechanical value to those. Just be fair about letting a Loremouse test provide insights about those other applications. For non-fight confrontations, I’d say the animals have diminished special advantage, but that’s no rule.
As for the second topic, I suggest gauging whether you want a recurring NPC or a single-show cameo. If you want all the foxes of a setting to seem more cunning, you can certainly append the trait to all cameos of any fox; I don’t think that’s a problem. But, if you are planning a recurring NPC, give that fox a name, perhaps some background of confrontations with mice, and append one or more traits.
For a single cameo, learning the trait can be included in a Loremouse test outcome. For a recurring NPC maybe a Loremouse test can learn about the trait, or maybe it is simply common knowledge about that named animal.
as a caution, the NPCs cannot gain checks by playing traits against themselves, so it would only ever exist to gain a benefit. This might just feel like piling on for players that will never see that NPC embrace a detriment from having a trait or two. Still, if they get to know an animal as a recurring NPC, they can learn about the trait and look for ways to mitigate or nullify that benefit.