Like Chansey, for example. Am I able to shiny hunt her via this glitch?
In order for Cute Charm to work, the target Pokemon must have a gender and have a non-100% male-female gender ratio.
Since Chansey is 100% Female, the Cute Charm Glitch will not work.
Source: https://www.smogon.com/ingame/rng/dpphgss_rng_part5