@Eirikr Please take a look at Etymology 2. Since the historical kana spelling is かはづ, should the phonemic(?) shape have been something like /kahadu/? --Dine2016 (talk) 13:52, 24 April 2018 (UTC)Reply
As Chinese, this uses the term 蝦蟆/虾蟆. There's nothing here that uses either the kanji 蛙 nor anything phonetic for kaperu.
The NKD entry uses a specific kundoku version of the Chinese sentence, specifically from the 熱田本訓(Atsuda(?)-hon Kun), referring to an edition of the Nihon Shoki from 1375, given as (emphasis again mine):
亦蝦蟆(カヘル)を煮て上(よ)き味と為
This is problematic on a number of levels.
亦(yì) is used in Chinese to mean also, which fits the meaning of the text. The Middle Chinese phonetic value was /jiᴇk̚/, the Japanese on'yomi are either yaku or eki, and the kun'yomi are mata or de mo.
蝦蟆/虾蟆(háma) is used in Chinese to mean frog; toad. The Middle Chinese phonetic values were /kʌp̚/ and /mˠa/. Japanese on'yomi of kō / ka and ba / ma / baku. Japanese kun'yomi of hamaguri and gama / buto / kuku.
This edition is from 1375.
So the phonology doesn't line up at all, and we have no clear basis for how or why -- or even if -- 亦蝦蟆 or 蝦蟆 were actually pronounced as kaperu in the Old Japanese text.
As an aside -- I confess I've had growing reservations about including Nihon Shoki and Kojiki first-citations in our etymology sections for yamato kotoba, due to the inconsistencies and uncertainties of the kun'yomi for these -- at least, when deriving from text sections written in kanbun.
For this specific 蛙 entry, I'm inclined to discount the Nihon Shoki source -- it's the wrong kanji, and we can't confirm the pronunciation.
@Eirikr: 亦(yì) may just be また(mata, “again”). Some words are spelled based off their Chinese semantics. For instance, 苦しい(kurushii, “painful, stressful, suffering”), was first cited to Shoki with the sense of mentally stressful and was spelled 塗炭/涂炭(tútàn, “great distress”, literally “be covered in coal”), but was pronounced kurusiki1, via it's 連体形(rentaikei, “attributive form”). This is probably why kaperu is spelled this way. Chuterix (talk) 02:59, 4 December 2022 (UTC)Reply
@Chuterix: The problem with attestations in the Kojiki or Nihon Shoki is that many of them are from kanbun, where the kun'yomi is based on kundoku versions of the texts from much later -- around the 1300s or so. If we can find attestations in the Kojiki or Nihon Shoki based on man'yōgana phonetic spellings (such as for OJP paya spelled as 波夜), then we are on much firmer ground.
Since we only have 蝦蟆 in the Nihon Shoki, and this spelling is not phonetic, we cannot use this as attestation for any kapyeru pronunciation. We can say that the Nihon Shoki includes the word 蝦蟆, and that this is traditionally read as kaeru, based on the kundoku edition of the Nihon Shoki from 1375.