I visited Glacier N.P. several years ago, and was able to rent an ice axe at a sporting goods/adventure store in West Glacier. My axe wouldn't fit in anyone's checked luggage!
I texted John from
Elevation Climbing in Lone Pine -- they rent gear, crampons, but NOT ice axes. He felt there was too much liability. But he offered to give you a really good deal if you call him. I would definitely give that a try.
Also, visit this link:
Links to important Whitney info and check the Ice Axe Use topics.
