It's not so much your height and leg length that matter, as it is your arm length and the terrain.
I'm 6'3" with shortish arms, and use a 75cm as a basic walking stick/cane on mellow glacier routes. But when it gets steeper then 75 is too long.
I think you'll find that your 80cm classic piolet is going to be too long for you in many situations. Plus, stashing it on your pack or behind your back gets to be problematic in steep terrain or scrambling because of its length.
But if that's what you've got, then go for it. It will be adequate, but not perfect. Workable. A 80cm cane and a 55cm for the steep stuff will work fine. You'll likely end up getting a 65-67cm ax after your trip.