Green’s Dictionary of Slang

willie n.5

also willy
[orig. in northern but non-dial. use]

1. [1960s+] the penis.

2. in fig. use.

In compounds

willie-warmer (n.) (also willy-warmer)

a small woolen ‘sock’ supposed to keep the penis warm.

willie-waving (n.) (also willy-waving)

[1970s+] acting, speaking or posing in an exaggeratedly macho fashion.

willy-welly (n.) [wellie n.]

[1990s+] a condom.

In phrases

wave one’s willie (v.) (also wave one’s willy)

[1960s+] of a man, to act in an exaggeratedly macho manner.