And interstellar war was something they had no experience with; NX-01 was launched as a pure research vessel
...Which fits perfectly! Apparently, "pure research vessels" were an utter novelty in a Starfleet that had existed for at least half a century already, in one form or another. What had its ships been doing until then? Why, making war, of course!
The major issue would be that before warp five engines, the wars would have been fought with enemies who came all the way to Earth. Archer extended the wars to enemies who did not.
"The Slaver Weapon" eliminates many aspects of "The Soft Weapon" that would have been in major conflict with the Trek universe. Essentially, we only need to deal with a handful that weren't previously mentioned in Trek:
- The Slavers existed as shown.
Since this happened a billion years ago, it has virtually no effect on anything elsewhere in Star Trek. The Slavers were said to have had subject species, which died along with them in a past war, but nothing is mentioned of the "pancidal" nature of that war, of the essentially telepathic weapon that necessarily terminated all
intelligent life everywhere
. Just the Slavers and their subject races died, is all. (And then "intelligent life had to evolve all over again", but this probably happens all the time everywhere anyway, and the remark in its Star Trek isolation carries none of its original Known Space significance.)
- Stasis Boxes exist as shown.
It's a weird alien technology, standard fare for Star Trek. It is furthermore portrayed as truly indecipherable, thus with no applications whatsoever, which is better than with most alien tech in Trek. It has yielded artificial gravity, but Spock never says for whom and when, so that's not a continuity complication. That's all Spock mentions as a benefit, along with one small-scale drawback that probably cost a dozen lives at most, so it's not really all that grandiose in scale, not in the Trek version.
- The Kzinti exist as shown.
Nothing wrong with three-meter kittycats who bear a grudge, have telepaths and nonsapient females, and despise herbivores and pacifists, not in the Trek context. We've seen weirder, and it has never had any cross-connectivity to other Trek biological or cultural weirdness. Our heroes just aren't into cross-connecting, save for very rare occasions such as the "Wolf In the Fold" bit about things similar to Redjac.
- The Kzinti fought four wars with humankind and lost all of them. The last one was two hundred years ago
from the viewpoint of the late 2260s or early 2270s. Conveniently, the scope of those wars would have to be really modest if the early mankind triumphed in them; automatically, then, these would leave no mark in the general history of the Federation, or even that of Earth, and Sulu would only bring up the insignificant scuffles to humiliate the Kzinti. For all we know, Earth only triumphed thanks to Vulcan help (that is, Vulcans did all the fighting), but Sulu would of course omit that bit - for two reasons: to emphasize that two of the captives of the Kzinti are fearsome, superior warriors, and to downplay that one of them is an even more fearsome one.
The only real problem there is the one of timing. But since Sulu is dribbling a lazy insult at the ratcats from one corner of his mouth anyway, this is the perfect time and place not
to take him completely literally. "Two hundred years ago" from the 2260s perspective could be more like 2100 or even 2150 than 2060 - that is, anything more than 100 years ago would do, really. Starfleet in Archer's time could be full of "veterans of the Kzinti wars" who'd go "Huh? We fought those, too?" when reminded of the fact, as the fight really was nothing to write home about. Archer probably had a comparable war or two during his televised mission...