So you want the two stars to be spectral class K and spectral class M.
Unless the planets in your star system are going to be lifeless and uninhabitable, you should restrict the stars to main sequence stars of luminosity class V, since it is usually believed that only main sequence stars can have planets with life.
Wikipedia has lists with properties of main squence stars of various spectral classifications and sub classifications.
The one for K class main sequence stars is here:
and the one for main sequence M class stars is here:
Unfortunately it doesn't give the diameters of the stars of various types. The diameter of a star is important to calculate how large it would look at a specific distance, such as the distance where a planet would be habitable.
The red dwarf star EBLM J0555-57Ab may be the smallest main sequence star known. It has a radius of about 0.08 that of the Sun, about 59,000 kilometers, smaller than Jupiter or Saturn, though many times as massive as those planets.
I believe that the maximum resolution of the human eye is about 30 arc seconds, or about half of an arc minute. An arc second is about 0.000000771 of a full circle.
So about 30 arc seconds would be about 0.000023148 of a full circle.
If the star EBLM J0555-57Ab is has a radius of 59,000 kilometers and diameter of 118,000 kilometers, for it to appear about 0.000023148 of a circle wide the circumference of the circle would have to be be 5,097,632,625 kilometers. So the radius of the circle would be about 811,314,115.6 kilometers. And that happens to be about 5.4233 times an Astronomical Unit or AU, the distance bwween Earth and the Sun, which is 149,597,870.7 kilometers.
Since an extremely tiny class M star such as EBLM J0555-57Ab would contribute only a tiny fraction of the heat and light that even the dimmest spectral class K star would, your planet would be frozen and lifeless unless it was close enough to the class K star to be within its circumstellar habitable zone.
Unfortunately, the circumstellar habitable zones of main sequence spectral class K stars are smaller than that of the Sun. It is possible that main sequence spectral class F stars could possibly have habitable planets with life. But even in the casse of an F0V star, the habitable zone would probably only extend to abut 3 AU from the star.
And of course the problem with being far enough away from the stars to not see the class M star as a disc would be similar to the problem of not seeing the separation between the two stars. As the two stars orbited each other, sometimes one star would be in front of the other, sometimes one star would appear to touch the other, and often the stars would appear to be separated.
You can't make the orbital period of the planet equal the orbital period of the two stars around each other so the two stars always have the same configureation as seen from the planet, since the planet would have to orbit the two stars at a distance at least several times as large as the distance between the stars. So sometimes people on the planet would see the two stars at their maximum separation.
There have been many questions about the habitability of giant, planet sized moons orbiting giant planets. Usually, those planetary sized moons are assumed to get their heat and light from the star in the system, and thus be orbiting within the circumstellar habitable zone of that star.
But scientific studies show that such a hypothetical moon could receive significant heat and life from the giant planet it orbits. That heat and light would be from the star's light reflected from the planet onto the near side of the moon, the infrared rays emitted by the planet at its temperature, and from tidal heating resulting from tidal interactions with the giant panet and any other large moons of the planet.
Those calculations showed that in some cases the moon could receive sufficient heating from the planet to suffer a runaway greenhouse effect and become uninhabitable. And of course if the planet and moon were farther away from the star in the system, that heating might be enough to keep the moon warm enough for life despite being outside the circumstellar habitable zone of the star.
So I think that you should make the two stars a very close binary, perhaps a contact binary, and make the habitable world a moon of a giant planet far beyond the usual outer ledge of the habitable zone, kept warm enough for life by tidal heating.
I suggest that you make the K type star in the system a K0V class star, the most luminous and hottlest subclass of K type star. The hotter a star is, the more intense its light will be, and the more painfull it will be to look at that star, and the brighter glare from the K type star will make it harder to notice the class M star.
In fact, you might want to reconsider and make the bigger star a class G star or even a class F star, since they would be hotter and thus harder to look at and make it harder to notice the M star beside it.
I don't know how advanced any civilzation of the planet will have to be to discover the smaller star. It is possible that people will notice fainter shadows from the smaller star pointing slightty away from the darker shadows from the brighter star.
Have you ever noticed the shadow of a tree on the ground with many spots of light on the ground where the light is passing trough gaps between leaf coverage? Long ago during a partial solar eclipse, I noticed that those spots of light on the ground were crescent shaped, like the Sun during the eclipse. So I think that would enable some people to notice that there is a smaller light source beside the main star.
So you should make the two stars as close together as possible, and make the giant planet with the habitable moon as far away from the stars as possible, to make all such effects as small as possible.
That means you need to look at previous questions about the habitability of exomoons and the answers to them, to figure out how to keep your exomoon warm enough to be habitable.