If it's just going to be refrigerated, I don't think the shrink bag will prevent spoilage any more than a loose plastic bag. Shrink bags are primarily used to keep the meat from freezer-burning by reducing the meat's exposure to air. When you aren't freezing the bird, plastic is used to prevent contaminants from contacting the meat, but it doesn't matter if the bag is tight.
We all have different standards for food hygiene. I've heard that in France, it's common to field-dress pheasants and grouse and then hang them in a cool shed by the head until the vertebrae in the neck separate, up to two weeks. Here's a pretty thorough discussion of hanging pheasants for as long as 10 days, in as warm as 55 degrees.
http://honest-food.net/2008/11/27/on-hanging-pheasants/
For my tastes, that's taking things a little too far, but it illustrates that some people have no problem with aging their meat, and it's not because they are ignorant of the risk of spoilage.
Another thing to consider is that brine not only improves the way the meat cooks, but also can discourage food spoilage.
I can understand not wanting to freeze it... then (IMO) it's no longer truly fresh, no matter how short a duration it spent in the freezer. If it were my bird, I think would try to butcher it a little closer to the day you are going to cook it, and then lightly brine it for a few days. I know you said you had a busy work schedule, but it doesn't take all that long to butcher a bird. The slowest part is waiting for the water to boil for the scald!