I don't think I would try cutting down the length of a self-tapping screw, but the idea of an aluminum screw is brilliantly simple and logical. The white head colour of this example is to match fencing, and the screws would look better without it, but the idea would be the same regardless of cosmetic finish.
My only concern would be if the screw is strong enough to take the torque required to drive it into the frame channel without losing its head. A test would be called for.
I tried a Home Depot search for just aluminum screws, and found only these:
#10 1 in. Phillips Pan-Head Sheet Metal Screws
The drive is Phillips (which I would not want), I don't know offhand what size would be right, and although the description says they are sharply pointed the photo shows self-drilling (which is not needed)... but it is a start which suggests that the ideal screw might be out there.
What thread size (diameter, such as #8 or #10) and length is suitable for the frames? I have similar window frames, but would rather not pull one out to check.