If you take a look at the map as a logistician would, that's a loooong way off and the Imperium would have a lot of warning during which they could build ships and activate reserves.
The K'Kree have no realistic invasion route to the Imperium coreward of Khuur, at the rimward end of Ley. Everything coreward of there requires a J5 fleet. The K'kree have to cross eight subsectors, with either diplomatic pressure ("hey there as you know we'll absolutely certainly murder you later for being G'naak but for now would you mind letting us establish a precarious logistics chain across your territory?") or many years of military invasion.
Either way, the Imperium has a lot of warning, and the K'kree have to learn how to operate at the end of a logistics chain as long as their current empire is wide, using their vast, expensive and technologically inferior ships and weapons* against a foe fighting only a few subsectors from their industrial core.
Also, some Vargr would probably launch the odd raid - you can't really talk in sweeping terms about such a diverse jumble of polities - but the Vargr anywhere near the Two Thousand Worlds do not want to see the K'kree dominate. Check out GURPS Traveller: Alien Races 2, for example, for info on how the two races view each other: it's much how you would expect borderline wolves and murderous vegans to view each other. Especially so in the case of the Red Vargr that are found at the Trailing end of the Vargr territory.
*Nominally they're not massively behind the Imperium but they have a far more shallow industrial base. "Most starships operating within K’kree space are built to TL9–11 standards." and "The majority of K’kree worlds are within the TL7 to TL11 range... However, this technological capability refers to the cities. On worlds with a‘shirtsleeve’ environment there will always be a segment of the population living a simpler life on a semi-nomadic basis. These herds make use of advanced technology but cannot produce it." - Both quotes from "Aliens of Charted Space Volume 1".