In order to make two bright objects look like one, you need them to be very close together (angular distance, at least, so their separation is small relative to the planet's orbital radius), and ideally close to the same brightness.
Here you have one that's significantly dimmer, smaller, and cooler than the other, so the best you'll get is to have the two stars so close together that one skims the other's atmosphere. The stars can then fill each other's Roche lobes, giving an overall "egg shape" to the pair (with the small end of the egg fairly sharp compared to the usual hen fruit), and the small end dimmer and redder. Exchange of gas between the two can further blur the distinction between the stars -- and of course people who evolved there will think it's entirely normal to have a star that isn't spherical or of uniform temperature.
What I don't know is whether main sequence stars in this proximity will affect each other's normal course of evolution, or whether the two will tend to equalize masses over geological time (or vice versa), make the smaller star unstable (or vice versa), etc. You'll need more astrophysics knowledge for that -- but it won't matter at all over the life of a human, a civilization, perhaps even a species (stars mostly change very slowly, and K and M type slower even than our Sun).
From comments (thanks, @Logan R. Kearsley), it seems that evolution of the stars won't be noticeably affected until the larger, shorter-lived star starts to leave the main sequence and blow up into a red giant, at which point the smaller star will steal mass and slow this process. How much this will affect the evolution of the smaller star (which would otherwise turn into a truly tiny white dwarf after a trillion years or more) is less clear; if it gains enough mass it might itself become a red giant in only a hundred billion years or less.
None of these stellar evolution changes will have any effect on a civilization on the circumbinary planet of this question, however; the lifetime of a K star (depending on its mass) ranges from almost twice to half a dozen times that expected of our own sun -- seventeen to seventy billion years, roughly.