Hmm, how to do the "Slaver Weapon" without the overt Niven elements?
Might have to pull an "Arena" on this one, having only the vague outline of the original narrative. Let's see...
Drop aspects about the Thrint and their slave species. So instead of an ancient weapon left by a long dead race, have it be what Spock and Sulu deduce, a spy's weapon, but it's a prototype being developed by Federation intelligence. Spock, Sulu and Uhura are tasked with transporting this device to a StarFleet base. Even they don't know what it is. Since it's Fed tech' and not a Slaver box, something else is needed to make them land.
Drop the Kzinti. Make them another adversarial species. Possible candidates could be Klingons, Gorn, maybe Romulans. (If this were the "Next Gen'" era, one could play upon the often bragged upon Klingon "honor". The leader get sidewhacked by Spock, a seeming pacifist and he'd demand a rematch. But since this was years before Ruffles had ridges, er, I mean Klingons, let alone the obsession with "honor", it might have seen odd. Klingons were portrayed as the "back stabbers" until '87.
Romulans might work as we observed a sense of fair play in Mark Lenard's "Romulan Commander". Maybe the leader here is disgusted with the way Vulcans socially developed sense their "split". Again, getting ambushed by a supposed peace lover would be insulting to a warrior race.
Given their teeth, I think we can reasonably assume the Gorn are likely carnivores. so, like the Chuft-Captain, the leader would be shamed getting injured by a plant eater.
Or, if one just has
to employ a feline species, build upon M'Ress' species. Make it a faction of Caitians that opposed the planet's entry into the Federation. The idea of milling about with carrion eaters and flat out herbivores is disgusting to them. they want to return to the "old ways". Again, the initial confrontation between the lead pirate and Spock can not go unchallenged. (While I personal like this twist, even i will agree that might lean a bit too close to Niven's Kzin for comfort.
Point is, the "meat" of the story could be retained while keeping it more firmly rooted in existing Trek lore.