They didn't include Sisko.
It would probably go like that:
Hostile alien: I'm going to rape your mom
Sisko: I warn you, this is a bad idea. Continue and we'll retaliate.
Kira: Our planet got raped by the Cardassian. We're gonna rape them so hard when we get the chance.
Hostile alien: And your dad
Sisko: Ok, guys, he is clearly hostile. Let's find a solution.
O'brian, Bashir, Odo, Dax, the Prophets, Nog, various secondary characters: We're on it!
The Klingon: We will help you, this alien also threatened to rape our mom
The Ferengi: Wait! We could make good money doing business with them. Oh, wait, nevermind, this alien tried to rape Quark.
Quark: I was trying to make money, but I was the comic relief character this week
Rom: I helped him.
O'brian, Bashir, Odo, Dax, the Prophets, Nog, various secondary characters: We got this solution, but it may not work.
Sisko: Dammit! If only there was a way for it to work for sure
Damar, Section 31, other various secondary characters: We can make sure it works for sure, but it will be unsavory and unethical.
Sisko: God damn it! Do what you have to do
Jake: Hi, dad, I'm here to provide some daily life interactions
Sisko: Thank you, son. So, who else will help us?
The Romulan: Nah, we're going to help them rape you and your family.
Sisko:... They said they'll rape your mom, you know?
Damar: It's true, they did.
The Romulan: WHAT! WE'LL RAPE THEM FIRST! WE'RE WITH YOU>During that time, various romantic plots and character developments happens
Sisko: Anything more?
the Prophets: The Sisko must trust the Prophets
Sisko: Okay, I'll do that. Thank you for your supernatural help, incredibly powerful being I'm the emmissary of.
Hostile alien: It's rape time!>Everyone start using the solution that was found to counter the alien>Hostile alien get fucked
Everyone but the alien: We won.
Happy ending, save from the sacrifices made