Exclude Shipping Tax in grand total

Question

I'm stuck trying to exclude the shipping cost from the order-totals table in the invoice email.

At the moment, the invoice email looks like this: (I included a little translation for the most important fields)

As you can see: the grand total (15.80€) includes the shipping tax (6.20€).

Is it possible (and if, how) to change the grand total to exclude the shipping cost?

I've made a small mockup below:

Do I need to edit template files? Or should I target the GrandTotal calculation in the model?

I'm using Magento 1.8.

I very much appreciate any help regarding this issue. :)