Sounds viable.
On the water...
I think your read that your motion doesn't matter is right. It's not analogous to the ineffective method of pointing a fan (from the stern) at the sails because... well, magic. In real life mounting a fan at the stern and pointing it at the sails doesn't work (well...1) because of the "reaction force" generated when the air is pushed forward.
But this spell clearly doesn't create a reaction force: the spell description contemplates pushing creatures away from the caster, but doesn't call out any "pushback" the caster feels. (Because he doesn't. Because magic.) So then "a line of strong wind... blasts from you." The plain reading of wind blasting from you is to say that "the air near you moves with some speed relative to you." You stand at the stern, look at the sails, and magically air behind the sails starts hitting them as a strong breeze emanates from you.
(How strong? The spell description gives us creatures in the area having difficulty walking (2'->1' typical "difficult terrain" rules). I equate this with the descriptor "effort needed to walk against the wind" given in the Beaufort Scale in the entry for "high wind, moderate gale, near gale." But the description also calls it a "strong wind," so perhaps we should look at the weaker Beaufort "strong breeze." Even then, it's 21-27 kts, or 35-46 fps.)
Now, hopefully you were running when you cast the spell, and you've just given yourself a significant boost. How significant a boost? That gets real complicated, real fast; @KorvinStarmast's answer does a good job of pointing out the tip of that iceberg.
1 - I really didn't want to get too much into the weeds on IRL fan-boating vs. magic fan-boating. The weird quirk being that IRL fan-forward works but is less efficient than fan-backward, whereas in magic-land the reverse is true!
At the table...
If you want to play out the chase at all, I recommend you discuss these plan with your GM ahead of time. Expecting your GM to be able to deal with windspeed differentials, point-of-sail issues, hull speeds, &c. on the fly may not yield you the chase scene you may be looking for.
Even if you don't want to game out the chase, you should give your GM a heads-up anyway. Even if you're content with a "good thinking, you get away with no trouble" your GM should have the opportuity to ponder how this will impinge upon your spell slots.
The Fog Cloud cannot be colored, RAW
Without circumstances dictating otherwise, spells in 5th edition D&D only do what they say they do, and no more. The Fog Cloud spell says it creates a 20' radius sphere of Fog, and that's all you can guarantee it'll do. If you want it to do more than that, you'll need a different spell.
You should be able to combine Fog Cloud, Light, and (optionally) Mage Hand to create the appropriate effect
Placing a colored light source inside the Fog Cloud should diffuse the light through the fog, creating the colored Fog Cloud of your choosing. Since of those three spells, only Fog Cloud requires concentration, it's possible for the same spellcaster to maintain all three effects simultaneously, and both Light and Mage Hand are cantrips, meaning you're not spending extra resources (other than your Action Economy) to produce this effect.
Simply cast Light (for the color of your choosing) on a rock, then use Mage Hand to lift the rock into the fog cloud (or simply place the rock inside the fog cloud if your character is physically able to do so). The range on Light extends at least 20 feet, and while it wouldn't disable the Heavily Obscured effect, it is plausible that a character could generate a colored fog cloud using this method.
Bear in mind that you may need a permissive DM to make this work, RAW, since the fog will surround the light, and while this should not obscure the light source itself, it's not clear that the physics of the light diffusing through the fog will result in the fog itself taking on the light's color. So it does require your DM to allow for real world physics to take precedence in this situation.
Best Answer
The spell cloudkill creates a "20-foot-radius sphere" and wind wall creates a wall "50 feet long, 15 feet high, and 1 foot thick".
So, each spell does exactly what they say it says it does.
If the Cloudkill were cast in front of the Wind Wall, it would be kept at bay, or, would it be dispersed as stated in Cloudkill?
This is how I would as a DM, with the information above. I would just as happy with a DM ruling the other way because this is an interesting edge case.
The strong wind from wind wall isn't acting like a normal wind, it isn't just blowing everything everywhere in the direction of the wind. So, it wouldn't blow the whole cloud away, but it would separate the cloud where it was cast. The sizes of these things matter. The wind wall would cut the cloud with a 1 foot line from top to bottom (assuming both were cast on the ground).
If the Wind Wall were cast down the center of an existing Cloudkill Would it be dispersed only in the area of the Wall? Or would the entire cloud be dispersed?
I personally would rule that the ony the 1 foot path would be carved out, as stated above, for the reasons stated above.