What are good alternatives to sunglasses for flying?
I've been flying for over twenty years. I've never once worn sunglasses or a hat in the cockpit, with exception of a view limiting device (i.e. hood). I understand why many pilots wear sun glasses and have nothing against it, but for me I feel like it hinders my vision more than helps. 

You can fly just fine without sun glasses. One thing that might help, is to make sure you wipe down your windshield before flight to make sure its clean and clear, in order to reduce glare. 

A baseball cap might be a good idea if your airplane doesn't have sun visors. 

You should be totally fine. Flying without sunglasses is like flying without noise cancelling headsets. Its a creature comfort, but not absolutely necessary for safe operation.