I don't think [med] is appropriate for ほくろ. It's an everyday word. No tag in GG5.
We don't use sk for ok readings. Those readings should either be dropped or split out into [arch] entries. I don't think they're worth recording.
こくし probably isn't uk. I'll make a new entry for it.

@@ -16,15 +15,0 @@
-<r_ele>
-<reb>こくし</reb>
-</r_ele>
-<r_ele>
-<reb>ははくそ</reb>
-<re_inf>&sk;</re_inf>
-</r_ele>
-<r_ele>
-<reb>ははくろ</reb>
-<re_inf>&sk;</re_inf>
-</r_ele>
-<r_ele>
-<reb>ほくそ</reb>
-<re_inf>&sk;</re_inf>
-</r_ele>
@@ -33 +17,0 @@
-<field>&med;</field>

I think it's just one sense. According to at least one kokugo こくし covers the mole sense too, so restraictiona aren't needed.

@@ -32,9 +31,0 @@
-<stagr>ほくろ</stagr>
-<stagr>ホクロ</stagr>
-<pos>&n;</pos>
-<misc>&uk;</misc>
-<gloss>mole</gloss>
-<gloss>beauty mark</gloss>
-<gloss>beauty spot</gloss>
-</sense>
-<sense>
@@ -43,0 +35 @@
+<gloss>mole</gloss>
@@ -44,0 +37,2 @@
+<gloss>beauty mark</gloss>
+<gloss>beauty spot</gloss>

https://www.wikiwand.com/ja/ほくろ
ほくろ（黒子、黶、英語:mole）は
...狭義の黒子（こくし、lentigo）と言い...

ほくろの特徴
https://kizu-clinic.com/services/ecphyma/mole
医学名：黒子（こくし）、

https://en.wikipedia.org/wiki/Beauty_mark
A beauty mark or beauty spot is a euphemism for a type of dark facial mark...

ほくろ	441521	65.4%
ホクロ	194305	28.8%
黒子	120944
こくし	35621	5.3% <-- largely unrelated terms
ほくそ	3082	0.5% <-- mostly? unrelated terms (ほくそ笑む)
ははくそ	148	0.0%
ははくろ	134	0.0%

https://furigana.info/w/黒子
ほくろ	92.7%
ぼくろ	5.6%
くろこ	1.7%

I encountered a "can you read this" quiz here. Japanese person couldn't read it offhand, but guessed with a little hint:
https://www.youtube.com/shorts/P8sz0ZY7eUU

Encountered 黒子 in the wild. Various entries are inconsistent with beauty mark vs. spot, the former seems more common, both seem fine to me in AmE.

I'm having a hard time finding any use of the [ok] readings outside of the kokugo entry itself. Google books turned up an interesting ref suggesting ははくろ, at least, is quite an old term indeed...
「ははくろ」が、長い間に「ほくろ」と形を変えたものでしょう.  ははくそ, ははくろ, and ほくそ seem possibly useful today only as etymology.

Suggest splitting med/col senses the same way we did for 脇芽.  I misspoke on another entry saying こくし was [ok] here.  Still, it is quite a bit rarer than the ngrams suggest, and maybe only appears as a medical term.  A couple of refs at least support this, and sankoku does not have こくし at all.

====
As a complete aside, I am wondering if Japan even has the "beauty mark" concept, which raises interesting glossing questions.

I found "モテるほくろ", which seems to be a bit of a neologism.  And this interesting headline (suggesting the answer to my question is "no"):
フランスでは、ホクロは美しさを引き立てるための道具だ。
https://ovninavi.com/664_corps/

@@ -12,0 +13,4 @@
+<reb>ホクロ</reb>
+<re_nokanji/>
+</r_ele>
+<r_ele>
@@ -17 +21 @@
-<re_inf>&ok;</re_inf>
+<re_inf>&sk;</re_inf>
@@ -21 +25 @@
-<re_inf>&ok;</re_inf>
+<re_inf>&sk;</re_inf>
@@ -25,5 +29 @@
-<re_inf>&ok;</re_inf>
-</r_ele>
-<r_ele>
-<reb>ホクロ</reb>
-<re_nokanji/>
+<re_inf>&sk;</re_inf>
@@ -31,0 +32,2 @@
+<stagr>ほくろ</stagr>
+<stagr>ホクロ</stagr>
@@ -34,0 +37,7 @@
+<gloss>beauty mark</gloss>
+<gloss>beauty spot</gloss>
+</sense>
+<sense>
+<pos>&n;</pos>
+<field>&med;</field>
+<misc>&uk;</misc>
@@ -36 +44,0 @@
-<gloss>beauty spot</gloss>

ほくろ	441521
黒子	120944
ほくろ除去	79932
黒子除去	143

@@ -6 +6 @@
-<ke_pri>ichi1</ke_pri>
+<ke_inf>&rK;</ke_inf>