I think the head cone thing might work. As man travels into space, he will take his canine brethren with him. Thusly surely Vargr will see canines with head cones on after surgery.
Not particularly likely that they would, on either score.
Taking another terran mammalian species adds a considerable number of additional vectors for local biome to reach humans. Of the various species we take with us, canines are amongst the top 10... and probably #1. (I'd expect horses, cats, and rats in the top 10 as well, tho' the rats may not be intentional.)
Most vargr, however, are unfamiliar with Humans other than as an abstract.
It's unlikely any given Vargr will have seen a Terran canid other than the ones "native" to Lair. And given the areas of primary overlap, they're Vliani influenced. Reducing the odds further.
And even if a Vargr has seen a genuine terran animal, how many of the will have been injured? (I've seen maybe 30 animals equipped with cones myself, and owned 3 of those... and the rest were at the veterinarian's office.)
In general, injured animals aren't common in public view.