It's unclear how this happened - all I know is that Dr. Duckie wanted an uglier tie than Wilson, but he failed. BUT, is this really Dr. Duckie? Is it their love child? I think Wilson and Duckie are like an old couple (you know, people start looking like their partner)?
SPECULATE.
(I'll stop spamming the group now)
ETA: How do ducks reproduce?
Birds have an opening called a cloaca that acts for both reproduction and excretion. They put their cloacas together in what is called a "cloacal kiss" and the male passes his sperm to the female this way to fetilize her eggs. Some birds such as waterfowl (ducks, swans, etc) and ostriches actually do have a penis that is internal when not in use.
Ergo: Wilson needs to engage in a cloacal kiss.