In my personal experience, not using a cotton-tipped swab for the task is like cleaning a plate loaded with gunk and burned-on patches with one's bare hands rather than choosing to use a sponge and/or brush. You can do it, [0] but it's much more work, much more time consuming, or you get an inferior result.
[0] In my case, I'd need to make one set of passes with paper wrapped around my smallest finger, and then another set with paper shaped into a tool that can lever the excess wax out from outer orifice of my ear canal.