So I'm 4 Weeks Post-op. Is my Nose Strong Enough to Return to Normalcy?

Nasal bones heal a little faster than other bones in the body. Four weeks is enough that you can return to most normal activities. The appearance is not however final at four weeks . It takes up to a year before all changes transpire.

At four weeks you are on your way to "normalcy" but I would give it some more time to be pushing and prodding the nose.  You really want to wait until the nasal tip softens before pushing too much on it.