中辞典

Let's have both.

@@ -16,0 +17 @@
+<gloss>bluish purple</gloss>

Daijs says: 
紺がかった紫色。濃い紫色。
Notice the *second* of the glosses, which is just "dark purple".  Seems a lot closer.

sankoku: 紫紺：ーの勇勝旗
紫色を、おぼいた紺色

Kuretake Ink-café MEIJI NO IRO "SHIKON" Ink Bottle 20g for Fountain Pens
https://www.amazon.com/Kuretake-Ink-café-SHIKON-Bottle-Fountain/dp/B0B2ZKC6GT?th=1

I think this is a machine translation:
https://woman.mynavi.jp/kosodate/articles/16482
A traditional Japanese color "紫紺 Shikon-means purple and navy-" is a dark, dark purple color with a hint of navy blue...
The best known example of the "紫紺 shikon" color is the championship flag of the high school baseball tournament in Japan. Every high school baseball player in Japan yearns for the "紫紺 shikon" flag of victory. In addition, "紫紺 shikon" is also the school color of Meiji University, and there is "Shikon song" in the cheering song of Meiji University.

Note: daijs actually offers: 濃い紫色

Anime character described as having 紫紺 eyes.

You might check out this color table, pretty cool. Standardize Japanese Color names(I think this converts shikon to RGB #470F4D, if I've converted the numeric RGB values correctly):
https://colors.japanesewithanime.com/japanese-colors/jis-colors

Here's a flag of this color.  Apparently this color on a flag signifies "victory". Sankoku used "ーの勇勝旗" as the example, which is why I thought to look for this.
https://meijinow.jp/meidainews/information/7346

Mercifully, even if I am not particularly adept with colors, I can google "purplish blue" and "bluish purple" and see that this is far from either of those.

I've come across a lot of questionable-ish color glosses here. I've shelved most of them for the moment, because debating color glossing in black-and-white text seems a bit quixotic. (I've considered suggested we throw up RGB values, 紫紺: approx. #470F4D, but in practice many historic colors will cover a range).  But this one seems pretty straightforward (and it's a color in common use).

Apparently a mix of murasaki (a very light purple):
https://colors.japanesewithanime.com/japanese-colors/紫-murasaki
and kon (~royal blue):
https://colors.japanesewithanime.com/japanese-colors/紺-kon

In English, I would call the result... (dark) purple. Nothing bluish about it.

Of course, there has to be disagreement, but these are all variations on dark purples:
#3C2F41
https://color-term.com/color/shikon-3c2f41/
#2b2028
https://icolorpalette.com/color/2b2028
#2E1031
https://www.color-sample.com/colors/172/

@@ -16 +16 @@
-<gloss>bluish purple</gloss>
+<gloss>dark purple</gloss>