I think that's a cool idea, and your dad would likely appreciate you putting your touch on it. I'll let J describe the technique probably better than I can because I pretty much go by feel, and also direct you to YouTube which is where I learned how, but I'll share my experience on the subject (I've done a handful of knives and some G-Shocks as well). First off, the color results can sometimes be hard to predict exactly, but I think in the case of that knife your idea could work well since the mint is such a light color and blue is darker. Expect the mint to possibly tint the resulting color somewhat though (I'm not exactly sure what mint and blue make). The "emerald green" dye might also make for a nice combo.
Here's an experiment I did with Rit "Sapphire Blue" over the green that comes on the LC200N Salt series. This picture captures it with the light hitting it perfectly and you can see the blue, but other times it just looks like a darker green fade.
I have the most experience dying the yellow Salt scales. On these I went with "Kelly Green" towards the pivot for the lime color, with an "Aquamarine" fade on the other end. Even though aquamarine is a bluish green, it didn't turn out very blue because yellow and blue make green. Longer dye times in this case didn't yield a bluer color but rather a darker color (with a hint of blue in some light).
That's not to say I'm suggesting the Native, I have no experience with it myself. I'm the wrong one to ask anyway, my dad has a drawer full of modern knives that I gifted him, but only ever carries the same Case he has for years

. Be sure to post a pic of your results if you do give it a shot though.