Unfortunately, as Japonic is its own language family entirely, it’s almost certainly a coincidence. But wiktionary gives some possible etymologies here

From Old Japanese. Found in the Nihon Shoki of 720 CE with the reading kaputo.[1]

Derivation currently unknown.

A surface analysis might suggest a derivation from 被る (kaburu, “to wear something on the head”). However, that reading derives from older form kagafuru and does not appear until 850,[1] some time after the first appearance of kabuto.

An alternative analysis might suggest a compound of 頭 (kabu, “head”, kun’yomi and native Japanese term) +‎ 兜 (to, “helmet”, on’yomi and borrowing from Chinese). However, the “head” sense with the kabu reading does not appear until near the end of the Muromachi period.[1]

Word-medial bilabial plosives usually underwent lenition, shifting along the lines of /p/ → /f/ → /w/, then vanishing altogether except where the following vowel was /a/. This lenition often did not happen at morpheme boundaries in compound words. The persistence of the /b/ in kabuto might thus suggest that this term was originally a compound of ka + puto. The ka element is uncertain, possibly the か (ka-) intensifying prefix added to adjectives; Old Japanese puto would be the stem and root of modern 太い (futoi, “thick; fat; stout”), possibly in reference to the protective strength provided by a helmet. This puto would then have undergone rendaku (連濁) to become buto.

Compare the phonology of adjective か細い (kabosoi, “very slender”), composed of this ka- prefix and adjective 細い (hosoi, ancient pososi) and demonstrating a similar retention of the bilabial plosive and rendaku (連濁).