This might help. It is a Hertzsprung Russell diagram created for the closest 1000 stars to the Sun, according to the 3rd catalogue of nearby stars by Gliese and Jahreiss (1991 http://cdsarc.u-strasbg.fr/viz-bin/Cat?V/70A ). I have labelled it with spectral types. EDIT: Now superseded by the Gaia catalogue - see edit at the end.
Although this catalogue is now getting a bit dated and there are now (smaller) catalogues of very nearby stars that are more complete, it still provides a pretty good census of the relative proportions of stars in the disk of our Galaxy near the Sun.
The wikipedia results you refer to tally quite well with the main sequence stars that dominate this plot. About 6% of the sample are white dwarfs, though this might be a lower limit because the Gliese and Jahreiss catalogue becomes demonstrably incomplete for an absolute V magnitude greater than 11. Less than 1% of the sample are evolved (sub)giants. There are no red (M-type) giants, so their occurrence rate must be smaller than a few in a thousand. It is difficult to provide a larger census because it is difficult to estimate the distance to stars outside of the solar neighbourhood.
In more distant populations (bulge, globular clusters etc.) the problems can be simultaneously easier and more difficult. Often you can assume all the stars you are looking at are more-or-less at the same distance, but you have problems with contamination and also that you just can't see the faint stars. The mix of spectral types depends on (i) the initial distribution of masses for stars born in these environments and (ii) the age distribution of the population (and also to a lesser extent on chemical composition). There is some evidence that initial mass distributions vary in the bulge and globular clusters from that in the disk, and the age distributions are certainly different. But the statement that the vast majority of stars are on the main sequence and heavily weighted to masses much lower than the Sun is still true.
The new Gaia satellite astrometry mission (first results in about 2 years from now) will sort many of these questions out because it will measure the distance to a billion stars with $V<20$.
EDIT: The Gaia catalogue of nearby stars
The catalogue discussed above has been almost entirely supersed by the Gaia EDR3 Catalogue of Nearby Stars. This contains a census of about 330,000 stars within 100pc of the Sun. The absolute colour-magnitude diagram of this sample is shown below - which illustrates the various evolutionary phases, main sequence, white dwarfs, red giants. Again, there are no red supergiants within 100 pc of the Sun - they are very rare. To use this catalogue you will need to understand the levels of incompleteness as a function of star type (the catalogue is not complete).
[An addendum, in the light of the comment from the question writer:
I understand the interest is in simulating the appearance of the Galaxy or at least representing its bulk light. To do this, then a modelling procedure might be the best way to go, but using a model that has been well tested against populations in our own Galaxy. A couple of possibilities occur to me.
The first is "Trilegal" - see Girardi et al. (2005) http://adsabs.harvard.edu/abs/2005A%26A...436..895G
- which will simulate photometry for any stellar field by combining mass functions, age distributions and stellar evolutionary models to provide Monte-Carlo HR diagrams like the one in my picture.
The second is the Besancon Galaxy model. This again offers the possibility of generating model HR diagrams and is possibly something you could make more progress with as they offer a web interface. They also show some faked Galaxy images generated from the model which I guess is very clse to what you are trying to do...