I can't believe you want the weight of your model to scale. As said above the material would have to be the same to get the same density and also you would need every peice of the titanic in your model! I think some of the washers would be microscopic. Why dont you just calculate the weight of the model, the weight to scale, subtract the weight of the model from the weight to scale, and add a peace of lead inside your model to compensate for the difference.

Really though, most people don't pick up their models and play with them so I'm not sure it will impress anyone.