"Ми шукаємо зелені туфлі."

Translation: We are looking for green shoes.

[UteEff]

Is взуття the more general word for shoes and туфлі a more specific one? From what I remember from Russian, I would guess that туфлі are women's shoes - am I correct?

[k00lagin]

Like you said, взуття is general and туфлi is more specific. It is general word for more formal kind of footware like loafers, oxfords, derbies, etc. There are also туфли on high heels, which are, mostly women's thing and include things like slingbacks, litas and so on.

[UteEff]

Дуже дякую.

[omniduo]

The correct word for ukrainian туфлі is dress shoes.

You can also use Мéшти. (accent mark on é is used just to show, that stress falls on the first syllable.)