A non-blanket offensive term for a wimp/pussy/girlyman

[Pentagathus]

Yo Exilianites, I need a top level brainstorm here.
Whilst playing a drinking game, if someone tries to wuss out I need a term that will offend them and them alone, usually I'd ask them if they need a tampon or imply that they are frightfully queer, but I can't really do that when I'm drinking with women and/or gays. I've thought about saying I've known schoolchildren that can handle their beverage better, but that kind of makes me sound like a paedophile.
Any thoughts?

[Jubal]

Animals tend to be good for such references

[Pentagathus]

That'll do donkey, that'll do.

[Gen_Glory]

is this term for refusing to play the drinking game or after agreeing to play, refusing to play properly?

[Pentagathus]

The 2nd one.

[Clockwork]

Not sure but the best term I've heard for a person that is properly blind drunk is shot smuggler

Or go with the Skyrim - Milk drinker