Green’s Dictionary of Slang

(US/Aus.) a man who firmly believes, all evidence to the contrary notwithstanding, that no woman can resist his charms.

1882		Dly Dispatch (Richmond, VA) 1 Nov. 3/3: The detective [...] pointed out to the newspaper-man [...] a ‘Billy Noodle,’ a would-be masher.
1890–1904		Farmer & Henley Sl. and Its Analogues I 198/2: billy noodle, subs. (American) [...] a fellow whose self-conceit leads him to suppose himself specially attractive to the other sex.
1895		Crowe Aus. Sl. Dict. 8: Billy Noodle, ‘a masher’; one who believes all the girls are in love with him.
1941		Baker Popular Dict. Aus. Sl.
1960		(con. 1950-1960) R.A. Freeman Dict. Inmate Sl. (Walla Walla, WA) 10: Billy-noodle – a spineless fellow who believes all the fluffs are madly in love with him.