The Radzyner Rebbe wrote three books about it, so that would be a good place to check.
Dr. Mendel Singer wrote an article about techelet, and in the course of the article, he mentions how the Radzyner Rebbe understood various sources in Chazal to refer to the cuttlefish. For example:
the requirement of once in 70 years, the
Radzyner Rebbe says this means that there are times when the chilazon is
And presumably there are times when the cuttlefish is abundant.
Hidden in the sand: The Gemara in Megilah states that the verse in Devarim
33:19, "sefunei temunei chol" ("hidden treasures of the sand"), refers
to the chilazon shel techeilet... On the other hand, it might
mean that it is hidden because it is buried in the sand. This is the
understanding of the Radzyner Rebbe, citing the Sefer HaKaneh (Hilchot
Tzitzit) as stating that the chilazon buries itself in sand with its
head sticking out.
And the cuttlefish buries itself in the sand.
Color of the blood: Rambam states that the "blood" of the chilazon shel
techeilet is black like ink". Rashi states that the appearance
of the "blood" of the chilazon shel techeilet is like the color of
techeilet. The Radzyner Rebbe reconciles the apparent contradiction
between Rashi and Rambam by explaining that when Rashi says maris damo,
"appearance of its blood", he is referring to the "blood" after it is
prepared for dyeing, while Rambam refers to the original color of the
And this is presumably true of the cuttlefish.
Treatment for hemorrhoids: The Gemara also tells us that the
chilazon was used to treat hemorrhoids.... Additionally, the Radzyner Rebbe had already written that
cuttlefish ink has been used as a treatment for hemorrhoids since ancient
times. Indeed, it is still sold today for this purpose.
So the cuttlefish is a good match.
Tentacles bent like hooks: The Mishnah describes a chain hanging on
the wall, with something called a chilazon attached to the head of the
chain. The mefarshim say it was called this because it was shaped
like the chilazon shel techeilet, and Tiferes Yisroel explicitly
states that this was an iron hook attached at the end which was used to
hang the chain on a wall. The Radzyner Rebbe understands this to mean
the chilazon has long tentacles that are bent like hooks.
Which apparently would match the cuttlefish.
The biggest problem, which disproves cuttlefish, is not archaeological. It is that its dye is not blue. And the Radzyner Rebbe was misled by an unscrupulous chemist. Basically, he asked this chemist to take cuttlefish ink and make it into a non-fading blue dye. And the chemist accomplished this by a process which basically broke down the molecules of the original organic material (via high temperatures) to the constituent atoms and added iron filings which combined with it, leading to ferric ferrocyanide, or Prussian blue. Start with ANY organic material (with carbon and nitrogen; for instance, human cells) and subject it to the process and you will end up with the same Prussian blue. So it is not coming from the cuttlefish specifically. So if this is the source and the process, why specifically the chilazon?
In 1913, Rabbi Isaac Herzog, then Chief Rabbi of Dublin and later the first Chief Rabbi of the State of Israel, as part of research towards his doctoral thesis, sent samples of the Radzyn tekhelet to leading chemists and dye experts in Germany, France and England for analysis. The results that he received were surprising. The experts determined that the blue dye of Radzyn was not organic in nature, but rather was the inorganic dye known as Prussian Blue, or ferric ferrocyanide. Herzog refused to believe that the Radzyner Rebbe would have purposely misled his followers and wrote to the dye masters of Radzyn asking for their process. Upon investigation, the solution to the riddle became apparent. The Radzyn recipe called for heating the squid ink to very high temperatures and then for the addition of iron filings. What in fact happens under these conditions is that the organic molecules break down and the constituent atoms of carbon and nitrogen recombine with the iron, yielding Prussian Blue dye. The squid ink is not an essential component for this reaction; any organic substance could be substituted, since the structure of the molecule is irrelevant and only the elemental components are utilized. Herzog could not accept the notion that the Talmudic requirement for a specific marine source, the hillazon, could be based on such an indirect and vague relationship. He therefore concluded that the Radzyn tekhelet could not be considered authentic.