Just to let you know the word kayn has more than one meaning. It means “none” as well as “to”
Usually when you use the word kayn for “none” it goes together with the word nisht a double negative.
The word Kayn “to” also intechanges with the Yiddish word in “to”
You can say
Mir zenen geforn kayn New York or
Mir zenen geforn in New york
meaning we travelled to NY
The correct sentence you were lookin for is
Mir veln aroys’geyn
We will go out
In the Yiddish system many words have prefixes or sufixes added on to the stem and it changes the entire meaning.
Where in English you would have 10 different words in Yiddish it can be the same stem with different prefixes added to it.
Yiddish is a fascinating and very expressive language and not extremely difficult to learn