All Japanese words (not characters) have kana pronunciations, but yes, for individual kanji characters, people use a specific type of dictionary called kanji di

All Japanese words (not characters) have kana pronunciations, but yes, for individual kanji characters, people use a specific type of dictionary called kanji dictionary (漢字辞典) and the order of this dictionary is indeed not (always) based on the pronunciation (stroke count of radicals is often used for the paper version). Here's an (online) example: https://kanji.jitenon.jp/ https://kanji.jitenon.jp/ On the right hand side of the above site, it shows the pronunciation (both on-yomi & kun-yomi) and the stroke count.