In Europe your will be hiking on altitudes less than 5000 m, and on these altitudes you can go with sunglasses without heavy specialized equipement.
However not any piece of sunglasses will do.
First, they have to be either made of glass (which stops UV rays) or special UV-proof plastic. Not every plastic stops UV rays, and if not, using it is even more dangerous than looking with bare eye: dark tint makes less visible light fall on your eye and the pupil gets bigger, accepting more UV light, which is not stopped by plastic.
Most of plastic sunglasses are made of more or less UV-protective plastic nowdays. You will need the ones with UV protection factor 4. It the sticker on your glasses just says "protects from 99% of UV" without mentioning the protection class (2,3,4), it is not enough. I would also make sure that the manufacturer is reliable, because if they cheat, it may cost you your eyes.
Second, you have to choose a model which blocks as much of side light as possible - they have to fit perfectly without gaps. No gap from below is absolutely a must, a little light entering from the top is OK (there is no snow there, he-he). You can also allow for a little light from left and right sides, but try hard to minimise it. Sometimes a little duct tape will help to patch the remaining holes, as Ben Crowell have said already.
Finding glases that fit you perfectly is not very easy, so you'll probably spend a lot of time at the stand and try a couple of dosens of models.
If your sunglasses are made from plastic with good UV protection and they fit you well (in terms of no holes), they are enough for European altitudes and you don't need anything else.
Bonus tip. If your drop and brake your glasses in the middle of the trail and the frame is more or less undamaged, you can improvise an UV-protectant solution by inserting paper instead of glass into the frame. Cut a narrow slot or hole in each "glass". You will be able to see something and block most of light at the same time.