I'm 6'0" with long legs and (apparently) short-ish arms. I got a couple used ice axes at a garage sale and am wondering what I can do with them. I have a pair of 55 cm ice axes, made by Cassin. They may be 80s or 90s stuff (I don't know, I wasn't around then). I was thinking of pairing one of these axes to use as an ice hammer with an 80 cm BD Raven of my dad's. I plan on using this to do a couple routes on Zugspitze, and to climb Gerlach in the Tatras. Does anyone have any ideas or comments on how well this would work? I'd like to avoid buying another axe. Thanks.

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.