Does removing a (non-cancerous) mole reduce the chances of skin cancer developing in that spot?

I used to go tanning in tanning beds and a large, asymmetrical mole appeared out of nowhere and grew within a short period of time. I got it checked recently by a dermatologist but she just looked at it and determined it to be non-cancerous. I don't like the way it looks and want to get it removed. If I get it removed will it also lessen the chance of skin cancer ever forming in that spot? Or does it matter if some of the mole is accidentally left over?