Your original question was whether you could paper piece your log cabin after having cut your strips. Usually for paper piecing you cut your pieces larger than the finished patch plus seam allowances and then trim after sewing to the paper. However log cabin patches are all very regular in width (one of two widths, in the case of the curved log cabin), so I think this plan would work if you line up your strips very carefully. I would try it out on one block just to see.
I agree with the others that paper piecing is not usually called for with a log cabin block, unless the strips are very narrow, or the fabrics are difficult to work with. However paper piecing does produce a very accurate block, and you might find that this method works best for you.