Ion-exchange vs Gel Permeation Chromatography for proteins
Since lysozyme is so well studied, your best bet is to search the literature and see what methods other people use. See this paper, for example. They report that lysozyme can be affinity purified on Sephadex, but they also reference other methods in the introduction that you could take a look at. 

Both of the methods you described sound reasonable. The only way to know which is best is to try them and see. In fact, the best approach, depending on your application, would likely be to use both methods for optimal purity. Even when I affinity purity a protein, I will still often perform ion-exchange as a polishing step.