To není správně česky. Ikdyž někteří češi tato dvě slova volně zaměnují, tak znamenají něco jiného. Popsáno je to zde: http://www.rozhlas.cz/plzen/jazykovykoutek/_zprava/konkurence-a-uzivani-tazacich-zajmen-jaky-a-ktery-v-soucasne-cestine--845635
Jaký? Proč Jaký? Nemluvim češtiny (Anglicky speaker here, hoping that's correct) . Neznám.
They mean something else, although also some native speakers (as gurfe right here) missuse them as synonymous in some contexts as well.
"Který" is mostly translated as "which (one)" and it is connecting with picking one person/characteristic from finite possibilities.
"Jaký" should be usually translated as "what (sort of)" and it asks about an unknown attribute or characteristic.
That means: "Jaký klobouk se ti líbí?" = "What sort of hat do you like?" - I probably expect a description of characteristics.
While "Který klobouk se ti líbí?" = "Which hat do you like?" - we are now probably standing in a shop and deciding, which one to buy.
And to your hoping that's correct - it isn't. We don't really use the phrase "I'm not a Czech speaker" but instead we would say either "Nemluvím česky = I don't speak Czech" or "Nejsem čech = I'm not Czech." And it should be "Nevím" instead of "Neznám." Neznám is only about people - "Znáš Petra Nováka? - Neznám." = "Do you know Petr Novák? - No, I don't (know him)." Otherwise, about knowing facts, it has to be "vědět" which means for negative and for me - "(já) nevím."