As it turns out, there are two small pentalobe screws holding the pin component of the Classic Buckle together, so with a pentalobe screwdriver, the portion of the Band that connects to the Apple Watch can be disassembled, slid into a standard pin-based Watch band, and reassembled.
Along with a compatible Apple Watch band, a tiny pentalobe screwdriver is also required to swap out the band, but those are available at little cost. With a Classic Buckle and the screwdriver, making a swap is as uncomplicated as simply removing two screws, pulling apart the connector, sticking the pieces into a**ther Watch band, and putting it back together again.