It's not at all clear to me what effect if any a 6% reduction in the earth's magnetic field would have on climate. There are too many factors for a non-expert to take into account. That's why I only looked at the black body model to get a feeling for how much the Earth's temperature might be expected to change due to a slight increase in average solar output.   From http://www.geomag.bgs.ac.uk/earthmag.html:

3 Characteristics of the Earth's magnetic field

3.1 Reversals

When a rock is formed it usually acquires a magnetisation parallel to the ambient magnetic field, i.e. the core-generated field. From careful analyses of directions and intensities of rock magnetisation from many sites around the world it has been established that the polarity of the axial dipole has changed many times in the past, with each polarity interval lasting several thousand years. These reversals occur slowly and irregularly, and for a period of about 30 million years around about 100 million years before present, there were no reversals at all. In addition to full reversals there have been many aborted reversals when the magnetic poles are observed to move equatorwards for a while but then move back and align closely with the Earth's spin axis. The solid inner metal core is thought to play an important role in inhibiting reversals. At the present time we are seeing a 6% decline in the dipole moment per century. Whether this is a sign of an imminent reversal is difficult to say.