A Pokemon's shininess is determined when you receive the Egg. So if you get the Egg, save, hatch it, and it turns out to be shiny, then resetting will have no bearing on whether the Pokemon is shiny or not. Odds of a shiny Egg are not modified based on how many you receive, as each is their own standalone. So, saying no to an Egg will not affect how long it takes to get a shiny.
Source: Experience, I received a shiny Egg once as well.
Hope I helped!