I believe I can give an answer for the specific part of where the quote comes from.

After doing some digging, I found the English version of the quote mentioned on Wikipedia in a citiation to the book "Yamamoto: The Man Who Planned Pearl Harbor", page 102, the notes in the original book indicate that the information was referenced from the Japanese book "Yamamoto Isoroku, Gensai no shogai" with reference to memories by Shigeharu Enemoto(榎本重治), the important details are the event occurred around June 1939 when the navy and army had disagreement over Japan entering the Axis Pact with Germany and Italy.

Now, the trail turns cold for me since I am unable to verify the "Yamamoto Isoroku, Gensai no shogai" reference. But all is not lost, using this information and some research, I am able to find the source and the original text of the letter in Japanese.

Found here.

http://sybrma.sakura.ne.jp/03yamamoto14.htm

Now the date matches as May 31, 1939 in a letter meant as a sort of last will and testament in case of death, there are further details on the letter that I can safely deduce(from my knowledge of Chinese while reading the Japanese, but I am not fluent in Japanese). I further cross referenced with a Chinese source(referred to as Chinese source A) that has the translated version in Chinese. So I am fairly confident on the sourcing with two sources for an internet comment.

Now, we extract the "Confucius quote":

In English(from pp 102, "Yamamoto: The Man Who Planned Pearl Harbor"):

As Confucius said, ''They may crush cinnabar, yet they do not take away its color; one may burn a fragrant herb, yet it will not destroy the scent."

In Japanese(via weblink above at http://sybrma.sakura.ne.jp/03yamamoto14.htm ):

語に曰く、丹可磨而不可奪其色、蘭可燔而不可滅其香と。

In translated Chinese(from Chinese source A, after converting simplified to traditional):

《論語》有言：“丹可磨而不可奪其色，蘭可燔而不可滅其香。"

For any Chinese or Japanese readers, it is immediately apparent that both passages are the same, with only minor difference since the underlying quote is in Classical Chinese, which is generally the same in both languages. The interesting part is "語に曰く" might be translated incorrectly in both Chinese and English versions(it says roughly "according to the Analects" in Chinese here), but I am not an expert on Japanese to tell, but some versions of this letter(in translated Chinese) seem to indicate that the phrase is not specifically referencing the Analects rather it is more accurately translated to something like "according to ancient sayings".

But let's move on to the meat of the issue, where does this quote come from?

It is from an author the lived in the North/South period in China, from author Liú zhòu(~560AD, Northern Qi) in book Liú zi【（南北朝，北齊）劉晝，《劉子•大質第三十六》】.

Here is the quote in C-Text and courtesy of Harvard Library for the digitized book.

https://ctext.org/library.pl?if=gb&file=134208&page=34

Now, is the translation accurate, sure, it is not inaccurate, but translating Classical Chinese is a very tricky matter.

I would hope my answer here lived up to the high standards of this sub, but my strengths are more research(especially when in Chinese) not writing format perfect journal published ready pieces. However, since the question here piqued my own interest to do my own research, and the results turned out something that is able to answer the question, I tried to type up an answer that meets the criteria of this subreddit.

Lastly, a comment on my own personal observations, I find that part of the reason of this type of misquoting is the language barrier, we all are aware Confucius did not write quotes in English but rather in Chinese(likely Classical Chinese) and Yamamoto likely did not write this letter in English(he did know English though) rather Japanese. So the idea is you need to get back to the original quote in its original form(or as original as possible), and there are often times ill translated quotes of such nature floating around, either Confucius said no such thing, or it is misattributed or extremely loosely paraphrased. The case here is that Yamamoto correctly quoted as character for character as possible, but the confusion was if the quote itself was referring to the Analects or just the Classical Sayings, but the origin of the quote is from a book published thousands of years later in China during the North/South period.

Sources:

Hoyt, Edwin P (1990). Yamamoto: The Man Who Planned Pearl Harbor. New York: McGraw-Hill.

Sorimachi, Eiichi. Ningen, Yamamoto Isoroku, Gensai no shogai. Tokyo: Hikawado, 1970. 反町栄一著，人間山本五十六 : 元帥の生涯，光和堂。

Chinese source A(book about World War 2 and Yamamoto Isoroku): 平立、其明，第二次世界大战山本五十六亲历记，1995。

C-Text source(original quote, see link:https://ctext.org/library.pl?if=gb&file=134208&page=34 ): Liú zhòu, Liú zi（南北朝）劉晝，《劉子•大質第三十六》

edit1.0: some housekeeping, and cleanup to aid readability for people only reading the English parts by providing as much information in English as well, only the title and author of Chinese source A remains untranslated. Issue is there is very inconsistent romanization in places of differing Chinese and Japanese pronunciation of stuff, especially since some references were taken from other sources, and since I am not fluent in Japanese.