Beth....Can you send us a picture of the cabinet? Thanks
I agree that a wider trim would help..it maybe difficult to match the light oak stain but even if it is a little darker l believe it will look fine..good luck .. send us a picture when you finish
Here are some good ideas: https://www.bobvila.com/slideshow/boring-bathroom-7-fixes-for-an-old-medicine-cabinet-48190
Add a lightweight trim like a picture frame. Home Depot carries composite that is more like a plastic and looks like wood in a ton of cool designs, leaves, dentil molding, ones that look like rope. E-6000 or Loctite will hold the trim directly onto the edge of the glass.
Paint it or surround with tile or some type of stone.
Here’s what we did: https://www.frugalfamilytimes.com/2012/08/our-frugal-bathroom-reno-updating-old.html?m=1