刺戟 is a valid form listed in most refs

@@ -12 +12 @@
-<ke_inf>&sK;</ke_inf>
+<ke_inf>&rK;</ke_inf>

Most refs give medical examples for "irritation". It could almost be another sense.

@@ -26 +26 @@
-<gloss>irritation ( of the body, e.g. from an allergen, from a wool sweater )</gloss>
+<gloss>irritation (esp. of the body, e.g. skin, eyes)</gloss>

刺戟	16667	0.2%
刺激	6989575	99.8%

https://www.wordreference.com/enja/irritating

I guess I am "disappearing" the 戟 kanji form, but it sure seems to deserve it.

Long-story-short on the rest: 刺激 means "irritating" in the skin-response-to-chemicals sense, but pretty much nothing else, and definitely not "annoying".  This term is widely misused by English speakers(this unadorned gloss predates jmdictdb), and I think needs some kind of clarification.  

====

I've spent a while looking at this entry, and 刺激性. Wordreference seems to have it figured out.  Under "irritation" in the E->J direction, where there are many potential glosses, 刺激 is limited to (cause discomfort to part of body)/(身体の一部).

irritate⇒ vtr	(annoy) (人) ～をイライラさせる、怒らせる、いら立たせる 他動
  (身体の一部) ～を刺激する、炎症を起させる 他動
  ex. This sweater's a bit irritating if you wear it next to your skin.

Under 刺激 they list:
irritation n	(skin reaction)

That seems a bit narrow. You can 刺激 any tissue of the body I think(lungs, eyes, nose, etc.).

The wikipedia entry for 刺激性 is all about chemical irritants. 刺激性's #1 use is for irritation of the body (skin, eyes, nose, lungs, etc.).  刺激性 as 刺激 + 性 for senses[2] and [3] here is comparatively quite rare.

The unadorned gloss of irritation has, I think, lead to a lot of poor translations. Just a handful of the many bad "examples" on reverso:
Filter packs screen out offensive and irritating Web pages. フィルターパックは攻撃的で刺激性のWebページをふるい落とす。
I have never in my life met someone so irritating.　私は刺激性の誰かに会ったことがない私の人生を持っている。
Please help me to solve this irritating issue by suggesting an optimum solution. ...刺激性の問題...
It is very irritating as you cannot watch your favorite video peacefully. あなたが好きなビデオを平和的に見ることができないので、とても刺激的です。
and on and on....
https://context.reverso.net/翻訳/英語-日本語/irritating

On that list of examples, 刺激性の問題 legitimately exists, but only as "the problem of(skin) irritants". (not "an annoying problem")
皮膚刺激性の問題も事実上ない
https://fams-skin.com/famsbook/famsbook-3621/

I'm open to any other ideas for clarification.

@@ -12 +12 @@
-<ke_inf>&rK;</ke_inf>
+<ke_inf>&sK;</ke_inf>
@@ -26 +26 @@
-<gloss>irritation</gloss>
+<gloss>irritation ( of the body, e.g. from an allergen, from a wool sweater )</gloss>

Ok, my bad.

@@ -11,0 +12 @@
+<ke_inf>&rK;</ke_inf>
@@ -26 +26,0 @@
-<gloss>irritant</gloss>