Green’s Dictionary of Slang

pee-willy n.

[? pee-wee n.2 (1)/pee-wee adj. + willie n.5 ]

(Can.) an effeminate man.

[US]Trimble 5000 Adult Sex Words and Phrases.
[US]B. Rodgers Queens’ Vernacular 73: stereotype effeminate homosexual [...] pee willy (pej, hetero sl, ’40s).