A "general" ice axe is typically 70cm long and used mainly for snow climbing and self-belaying on steep hard snow. When I was in CO climbing 14ers, I started very early in the season and typically climbed long snow gullies, I self belayed myself with one 70cm tool backed up by a shorter 50 cm tool designed more for ice. The only time I have used an ice axe for hiking in the Whites, is spring climbing the snowfields on the cone of Washington, the winter route on Lions head and right gully in Tuckerman ravine. The shorter Technical axes are designed for steep ice climbing and would rarely be used on the 4ks. In the two pictures you showed, a 70cm general axe would be sufficient with good traction as well.