I always heard it as "cobbler's children ...".

Most kokugos have this expression.
The smaller dictionaries describe it as fussing over the well-being of others (他人の世話…; 他人のためにばかり…) at the expense of one's own well-being. They don't really mention the "specialist skills" aspect. I'm not sure how accurate that gloss is.

〈紺／こう／コウ〉〈屋／や／ヤ〉の〈白／しろ／シロ〉〈袴／ばかま／バカマ〉

Google N-gram Corpus Counts
╭─ーーーーーーーーー─┬───────┬───────╮
│ 紺屋の白袴　　　　 │ 8,333 │ 94.7% │
│ 紺屋のしろばかま　 │   237 │  2.7% │ - add, sK
│ 紺屋の白ばかま　　 │   111 │  1.3% │ - add, sK
│ こうやのしろばかま │   115 │  1.3% │
╰─ーーーーーーーーー─┴───────┴───────╯

Adjusting the glosses and gloss tags to match our usual style.

@@ -5,0 +6,8 @@
+</k_ele>
+<k_ele>
+<keb>紺屋のしろばかま</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>紺屋の白ばかま</keb>
+<ke_inf>&sK;</ke_inf>
@@ -12,3 +20,4 @@
-<gloss g_type="fig">the shoemaker's children go barefoot</gloss>
-<gloss g_type="lit">the dyer wears white</gloss>
-<gloss g_type="expl">specialists often fail to apply their skills to themselves</gloss>
+<misc>&id;</misc>
+<gloss>the shoemaker's children go barefoot</gloss>
+<gloss>specialists often fail to apply their skills to themselves</gloss>
+<gloss g_type="lit">the dyer's white hakama</gloss>

@@ -13,1 +13,1 @@
-<gloss g_type="lit">The dyer wears white</gloss>
+<gloss g_type="lit">the dyer wears white</gloss>

GG5

* Rearrange so expl at end
* Front with “shoemaker’s children”, which is usual English for this
(Heard in conversation)
BTW, compare 医者の不養生

@@ -12,1 +12,1 @@
-<gloss>specialists often fail to apply their skills to themselves</gloss>
+<gloss g_type="fig">the shoemaker's children go barefoot</gloss>
@@ -14,0 +14,1 @@
+<gloss g_type="expl">specialists often fail to apply their skills to themselves</gloss>