When Larry Niven opened his sandbox to fellow kittycat enthusiasts, the Man-Ktzin Wars
novels soon spawned their own curious micro-continuity wherein the first of the four wars consisted of four mini-wars of its own: four separate fleets launched to subdue Earth, each failing in an interesting scifi manner.
In the Trek context, these Four Fleets could quite nicely equate to the four wars Sulu mentions. Nothing in "Slaver Weapon" suggests the Kzinti of Star Trek would have been lacking FTL drives like their Known Space counterparts. But if they did, each Fleet would indeed have to wage its own war. The timeline might be quite compact, the four engagements put together spanning just a decade, and only a particularly spiteful person such as Sulu in the episode would insist on referring to four defeats, rather than just one general failure.