I ever did RNA extraction for tissue even it was not cornea, but i think this way might be possible for your tissue sample. I used mortar and pestle. Put your enough tissue sample inside the mortar (if it is possible, cut your tissue into small pieces at the beginning), then pour enough liquid nitrogen and mash it while it's immersed in liquid nitrogen. At the end, that's suppose to be dried and you will get powder-like sample. Put it in eppendorf or any processing tube. After that you can do the RNA extraction by following the protocol that you use.
I hope this sharing could be helpful for your experiment. Good luck!
Use liquid nitrogen and pulverize your sample. Pour in your mortar & pestle and grind. It can be done with glass as well (pyrex I believe) Check it w/o sample first.