However if you did manage to create a vaccum, there are a couple of things that you appear not to have taken into account.
Firstly, the weight of the air. At 1kg/m3 - and given that this box weights a kilo so is probably a good size - there are a couple of grammes you'll be loosing. (Significant in relation to the 10g of bird anyhow!)
Secondly the bird is likely to start to dry out significantly in a vacuum, as moisture will be extracted to fill the void as it were, caused by the pressure within the presumably ex-bird's cells. This again is likely to have a significant effect on the accuracy of your figures, as mammals are made of what - 60% water?? I remember not!!!
So in summary Mr B, I think that your method is terribly flawed, and think you should come up with a better alternative!