There are plenty of push start button kits around but the majority still require a key. I expect a full replacement will be fairly costly.
Your key could well have a transponder for an immobiliser integrated also, i'll admit to knowing nothing about the z3. Maybe you could look into a new alarm/immobiliser system . I remember the old clifford ones were modular and you could add or remove bits like intellistart, full closure etc. There may even be one which can replace your key all together. Just a thought.