I am actually reading your question differently than the other posters. I've had laser hair removal done in a dermatologist's office by someone who is licensed to do this. They always have US wear the safety glasses, but she does not. I asked her about this and she told me that she looks away when she presses the button.
That being said, she's a professional and knows all about the system SHE uses. And she knows exactly how to look away. You aren't a professional and you don't know what she does...
I think that what you are saying is that you are worried about the bright light and wonder if you should be wearing glasses. I don't think you're saying that you are going blind, but that you are concerned about habitual use of the device because of the light.
IF I am understanding you correctly, then go ahead and call the customer service number and talk to them. And it couldn't hurt to wear the kind of glasses that would be appropriate for this...