カジヤ isn't used for sense 1.

@@ -23 +23 @@
-<re_nokanji/>
+<re_inf>&sk;</re_inf>
@@ -34 +34 @@
-<s_inf>usu. カジヤ</s_inf>
+<s_inf>usu. written as カジヤ</s_inf>

Never heard them called that.

@@ -22,0 +23 @@
+<re_nokanji/>
@@ -33 +34,3 @@
-<gloss>cat's paw (small crowbar for pulling nails) (usu. カジヤ)</gloss>
+<s_inf>usu. カジヤ</s_inf>
+<gloss>small crowbar for extracting nails</gloss>
+<gloss>cat's paw</gloss>

https://en.wikipedia.org/wiki/Cat's_paw_(tool)
A cat's paw or cat's claw is a metal hand tool used for extracting nails, typically from wood, using leverage. A standard tool in carpentry, it has a sharp V-shaped tip on one or both ends, which is driven into the wood by a hammer to capture the nailhead. Essentially, it is a smaller, more ergonomic, purpose-designed crowbar.

https://dictionary.goo.ne.jp/word/鍛冶屋/
２ 釘を抜くのに用いる、鉄棒の一端がL字形に曲がり、釘を挟む割れ目のついた工具。

I'm not sure how to mark it, but [2] is usually written in katakana specifically (and [1] probably never is...). You see this in shopping results, and on product labels. I doubt kanji are ever used for [2] in practice.

It seems that this matching (カジヤ = "cat's paw") is new information to the internet. But I'm fairly confident on this one.

Colloquialism for colloquialism(although, I guess the English has become more of a legitimate term).  The definitions exactly match from daijs and English wikipedia.  There is actually a picture in sankoku, and I recognized it immediately. I framed houses in college, and always had one on my belt.  A cat's paw/かじや is a mini crowbar for yanking nails out of things (you hammer the head straight into the wood, then pry the nail out).

Here's a カジヤ :
https://www.monotaro.com/g/00543119/
Here's a cat's paw (of all things, a Japanese import, but that's a coincidence):
https://tftools.com/en-jp/products/mokuba-precision-japanese-cats-paw-nail-bar

Second link has a video of the tool in use, not that it matters.

"prybar" and "crowbar" alone are more ambiguous than necessary.  If you see カジヤ in Japanese, you immediately know its size and purpose (it is not a 3-foot long crowbar, for example).

@@ -20,0 +21,3 @@
+<r_ele>
+<reb>カジヤ</reb>
+</r_ele>
@@ -30,2 +33 @@
-<gloss>crowbar</gloss>
-<gloss>pry bar</gloss>
+<gloss>cat's paw (small crowbar for pulling nails) (usu. カジヤ)</gloss>

WWW images.

@@ -28,0 +29 @@
+<misc>&uk;</misc>

kokugos have a second sense.

koj: 釘抜きに用いるL字形の鉄梃。
sankoku: 〔俗〕箱などの くぎを ぬくときに使う、先がＬの字形に曲がった道具。

〈鍛冶／かじ／カジ／鍛治〉〈屋／や／ヤ〉

Google N-gram Corpus Counts
╭─ーーー─┬─────────┬───────╮
│ 鍛冶屋 │ 238,085 │ 69.4% │
│ カジ屋 │  29,258 │  8.5% │ - add
│ 鍛治屋 │   6,620 │  1.9% │ - add, sK (meikyo: 「鍛治屋」は誤り。)
│ かじ屋 │   3,417 │  1.0% │ - add, sK
│ 鍛冶や │   3,068 │  0.9% │
│ 鍛治や │     180 │  0.1% │
│ かじや │  37,597 │ 11.0% │
│ カジや │  21,876 │  6.4% │
│ カジヤ │   2,810 │  0.8% │
╰─ーーー─┴─────────┴───────╯

@@ -5,0 +6,11 @@
+</k_ele>
+<k_ele>
+<keb>カジ屋</keb>
+</k_ele>
+<k_ele>
+<keb>鍛治屋</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>かじ屋</keb>
+<ke_inf>&sK;</ke_inf>
@@ -14,0 +26,6 @@
+<sense>
+<pos>&n;</pos>
+<misc>&col;</misc>
+<gloss>crowbar</gloss>
+<gloss>pry bar</gloss>
+</sense>