A Pokemon's shinieness is determined when you receive the Egg. So if you get the egg, save, hatch it, and it turns out to be shiny, then you are able to reset the game, and the Pokemon will be shiny no matter when you hatch it. 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!