How long would it take for a changing mole to become cancerous and spread?

It's moot: If a mole is changing, or shows any sign of being a melanoma, you need to make an appointment and be seen now. I would not accept a waiting period of more than two weeks, and would try to be seen at once. Progression from a benign-looking mole into a lesion capable of metastasizing is known to take as little as a few months. Get seen now.