We don't have synonyms for whether yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are wether, whetter and thether.
°Used to introduce an interrogative content clause (indirect question) that consists of multiple alternative possibilities, and indicate uncertainty between them; if.
"He chose the correct answer, but whether by luck or by skill I don't know."
°Used to introduce a yes-or-no interrogative content clause (indirect question) that consists of a single possibility, and indicate uncertainty over it; if, whether or not.
°Used to introduce an interrogative content clause (indirect question) that consists of multiple alternative possibilities, and indicate uncertainty between them; if.
"He chose the correct answer, but whether by luck or by skill I don't know."
°Used to introduce a yes-or-no interrogative content clause (indirect question) that consists of a single possibility, and indicate uncertainty over it; if, whether or not.