Nothing bad would happen to you if you don't blink while you sneeze.
But unless you actually hold your eyelids open while sneezing it's likely that your eyelids will close as a natural response and reflex to sneezing.
I cannot ever sneeze without blinking even though I tried to and I think it's probably because your eyes are supposed to close and blink to protect your eyes from the flying germs that come out of your nose.
So you could hold your eyes open and sneeze and nothing bad is gonna happen but it's best to blink when sneezing like we naturally are supposed to do.