Not the best way to install your new floor. Technically, you could glue an engineered floor over your existing strip flooring if you run the new floor perpendicular to the old one, but chances are the new layout won't look right in your home. Plus, old 1" strip flooring typically has gapped up quite a bit and many times isn't fastened all too tightly.
Cherry is expesive, so I'd recommend installing a new plywood subfloor and doing the job right. Hope this helps!