Retaining shape area and length values in attribute table after a polygon projection?

Good afternoon all,

I have been projecting polygons between GCS OSGB 1936 and WGS 1984 Web Mercator Auxiliary Sphere and the shape_area and shape_length fields in the attributes table change after projection.

I understand that this is due to distortions/change in datum etc, however I was wondering if its possible to retain the values of the old projection?

Is the only answer to copy/paste the original values pre-projection into new fields post-projection and delete/ignore the new values?

Many thanks

RL