There is an eyelash curler that I use that I love so much, but it's kind of hard to find. It is by Tweezerman brand and it is made out of plastic materials. It doesn't have a "boxed-in" area where you curl your lashes. It is open and it doesn't have a severe roundness to it either. It is designed specifically so it won't pinch. I found mine at an Ulta store, but you can look anywhere Tweezerman products are sold. Unfortunately, Sephora doesn't carry it.
I hope this helps.
I know what you mean, since Asian lashes can be especially short, stick straight, and/or resistant to curling. I suggest looking at eyelash curlers manufactured by Asian cosmetics brands, which have been made with an Asian consumer in mind. My favorite, the Shu Uemura eyelash curler, is a cult classic. The shape is perfect for going around your eye without pinching.
Well first off the issue is not that you're Asian but that your eyelashs are a bit on the short side. If I were you I would take a look at mini-eyelash curlers, They're around half the size of regular eyelash curlers so you'll have more mobility.
It might also help you if you lift your lid a little with your finger as you use your eyelash curler so you'll get the roots of your lashes better.
Hope that helps!