FWIW, OED3 hasn't reached "cashew" yet; for "mahogany" it doesn't cite forms that have direct bearing, so this is only to rule something out--

Etymology: Origin uncertain and disputed; earliest attested in 17th-cent. English writings about Jamaica (see below).
Perhaps ultimately a borrowing of Arawak maga mahogany (1528 in a Spanish text from Puerto Rico), or perhaps of a cognate or by-form of that word (see especially G. Friederici Amerikanistisches Wörterbuch (1947) 366–67). A derivation < Yoruba oganwo , in Nigeria applied to the genus Khaya (see sense A. 1a), has also been suggested (for summary see F. B. Lamb in Amer. Speech (1967) 42 219–26); however, this theory has not met with widespread acceptance (see especially K. Malone in Econ. Bot. (1965) 19 286–92).

The English word was adopted into scientific Latin as a specific epithet by Linnaeus ( Systema Naturæ (ed. 10, 1759) II. 940) as mahagoni, and is probably the source also of the continental forms: French mahogani, mahagoni, mahogon, etc., Italian mogano, mahogano (mogogano, magogano, etc.), Portuguese mógono, mogno, German mahagoni, Dutch mahonie, Swedish mahogny, Danish mahogni. Compare Spanish caoba < Taino kaóban.

(Of course it'd be K. Malone dissenting--sometimes brilliant, sometimes apparently utterly deluded.)