I know that not all Green (or any other color) Lanterns wear physical rings, but most do and that seems to be the case historically as well. I'm curious as to whether or not there's a canon explanation as to why they wear rings specifically?
They aren't all rings. Some Green Lanterns don't even have fingers. The ring can take the shape necessary to be close to the body of the wearer. Given the diversity of the alien races in the DC Universe, it would be hard to create a single form that would work for every creature shape possible. A ring isn't universal, it is merely convenient for many but not all species.
- In Universe: In the DC Universe, there are a preponderance of humanoid creatures with bilateral symmetry, perhaps it is simply a convenience or conceit on the part of the humanoid Malthusians/Guardians to design them as rings.
- Out-of-Universe: The character of Alan Scott, the original Green Lantern was designed on the common genre trope of the "ring of power". Since the update to the Golden Age Green Lantern was the Silver Age, Hal Jordan, the design was changed but the basic form remained the same.
Hal Jordan on the left, the Golden Age Green Lantern, Alan Scott on the right.