We call them danishes in Australia too. Accepting either "danishes" or "Danish pastries" should cover pretty much all English speakers.
Your suggestions are wrong. "Pastries" is not specific enough and a "patisserie" is the shop where pastries and cakes etc. are made and sold.
leivos = a pastry (pl. leivokset)
konditoria = a patisserie
viineri = a danish / a Danish pastry
Haluan ostaa viinereitä ja muita leivoksia konditoriasta.
I want to buy danishes and other pastries at the patisserie.