かしわ手を打っ	426

Leading with 柏手を打つ seems sensible to me. I note that most of the JEs only have 柏手 for かしわで.
Brian, for future reference, clicking to the last page of search results on Google doesn't give you the "true" number of hits (unfortunately). Google never retrieves more than a couple of hundred results for any given search query. I only get 197 results for "cat" after reaching page 20.

@@ -8,0 +9,4 @@
+</k_ele>
+<k_ele>
+<keb>かしわ手を打つ</keb>
+<ke_inf>&sK;</ke_inf>

sankoku: only kanji for かしわで is 柏手

Kanjipedia gives 柏手 for term "かしわで". 
Notes: 「拍手」とも書く。
https://www.kanjipedia.jp/kotoba/0005629300

Google search for:
"柏手(かしわで)"　(reached page 22, 213 results)
"拍手(かしわで)"　(reached page 19, 183 results)

Google image search for かしわでを打つ will give both results.　On a large screen of results, I got 22 pages with 柏 in the title/summary, and 7 with 拍.

Google news
"柏手を打つ" 4 pages, 35 actual results
"柏手を打ち" 3 pages, 22 actual results
"柏手を打った" 1 page, 7 results 

"拍手を打つ" 2 pages, 19 actual results
"拍手を打ち" 2 pages, 12 actual results
"拍手を打った" 0 results 

n-grams:
柏手を打って	1332　probably almost always かしわで
拍手を打って	1324　some mix of かしわで and はくしゅ

柏手を打った	330　probably almost always かしわで
拍手を打った	318  some mix of かしわで and はくしゅ

はくしゅを打つ	No matches
かしわでを打つ	29

Video game article, including non-religious "clap" form of 拍手を打ち(はくしゅ)
https://blog.ja.playstation.com/2019/08/05/20190805-sfv/
【Vスキル】
猫だまし
顔の前で拍手を打ち、相手を驚かせながら攻撃するVスキル。ヒット・ガード時は必殺技でキャンセルが可能。拍手の衝撃で飛び道具を打ち消すことも可能だ。

Wikipedia has an article 拍手 (神道), but prefers *both* the 拍 kanji *and* the はくしゅ reading, so it isn't really making a claim about the kanji for かしわで or the expression with を打つ.
拍手（はくしゅ、かしわで）とは、神道の祭祀や神社・神棚など神に拝する際に行う行為である。柏手と書かれることもあるが、誤りである。また、開手（ひらて）ともいう。
https://ja.wikipedia.org/wiki/拍手_(神道)

Wikipedia use of はくしゅをうつ reading in this *literal*, no-religious sense (same article), explaining the origin of the custom:
なお古代人は挨拶をする際に拍手を打つことで、手の中に武器を持っていないこと、すなわち敵意のないことを示し、相手への敬意をあらわしたという説もある[要出典]。

Book: 神社で拍手を打つな!
https://www.amazon.co.jp/exec/obidos/ASIN/4121506707/presidentjp-22

Article on previous book: ｢神社で柏手を打ってはいけない｣納得の理由
https://president.jp/articles/-/30958?page=1

「柏手」＝「はくしゅ」？「云々」＝「でんでん」？読み間違いが多い漢字5選
https://classy-online.jp/lifestyle/21399/
神社に参拝した際に、手をパンパンと打つことを「柏手」と言います。パッと文字を見たときの印象から「はくしゅ」と読んでしまいがちです。
「柏手」の正しい読み方は「かしわで」です。
そもそも「柏手」は「拍手」の「拍」を「柏」と書いてしまったことが語源と言われていますが、現在では「柏手」という言葉として広く伝わっているので、思わず「はくしゅ」と読んで恥ずかしい思いをしてしまわないように気をつけましょう！

神さまを拝むときに拍手（かしわで）をうつのはなぜですか
https://shinmeiguu.com/faq/faq-0-25/

I am only re-ordering relative popularity. There is already a separate entry for かしわで in this dictionary, and it already orders 柏手 ahead of 拍手. If this change seems controversial, I'm willing to go out polling Japanese people. There is the potential that I am mistaken, but to the extent that this is an entry for the "word" かしわで, I think the primary kanji are 柏手, and I think the references support this. 

I was motivated by the fact that  かしわ "Japanese emperor oak tree" is a super-odd reading for 拍, and *the* reading for 柏. I spent two hours googling around. If I understand correctly, *apparently* a long, long time ago, maybe someone wrote 柏手 instead of 拍手(ancient typo), and then people later read that typo かしわで, and this may be how the term came into existence.  柏手 should almost exclusively be ceremonial religious clapping, and I *think* almost always pronounced かしわで(though the 音読み is はくしゅ).

There is a recent book "神社で拍手を打つな", which uses the 拍 kanji, but it *also* gives furigana on the cover to avoid the natural はくしゅ reading.  However, an article in the popular magazine "president" on the book has the title "｢神社で柏手を打ってはいけない｣", switching kanji. (though it also gives furigana for かしわで in the article, non-jouyou). It is definitely apparent that both kanji are used though for かしわで.

n-grams are complicated because, among other things はくしゅを打つ is also valid (but only with 拍手), and 拍手を打つ is *a* way (if uncommon compared to 拍手を送る) to express "clapping" in general. (Example given with a news article on  "Street fighter Arcade edition(video game)". Maybe just the "act of clapping the hands together" (as in the video game reference), rather than "applause".

If I'm to believe the friendly article at classy-online, 柏手 should not be read  はくしゅ, and if I trust the shinmeiguu.com article, when used for clapping in prayer,  拍手 should be かしわで(not はくしゅ）. So *hopefully* this entry does not need the further complication.

@@ -5 +5 @@
-<keb>拍手を打つ</keb>
+<keb>柏手を打つ</keb>
@@ -8 +8 @@
-<keb>柏手を打つ</keb>
+<keb>拍手を打つ</keb>

gg5,etc.

栢手 is itaiji, but all hits come from edict.  拍手 gets most hits

@@ -4,0 +4,3 @@
+<k_ele>
+<keb>拍手を打つ</keb>
+</k_ele>

大辞林第二版
新明解第六版

@@ -5,1 +5,1 @@
-<keb>栢手を打つ</keb>
+<keb>柏手を打つ</keb>

Added additional PoS via batch update.Added additional PoS via batch update.
-*- via bulkupd.py -*-

@@ -12,0 +12,1 @@
+<pos>&v5t;</pos>