Not sure I agree with your statement. Most dealership actually prefers you to finance, as they can collect your interest as additional revenue in your car sales. Using cash will probably only help in direct person to person sale to help negotiate the price down.

As to OP's question: it depends a lot. Are you buying new, used, from dealership or individual? Spend a few minutes researching what the fair market sale price of the car in your area to understand your negotiation power. To be concise: if you find that the vehicle in question listed for $12k usually sells for around $11k in your area, you will probably not be able to buy it for $10k regardless of your method.

If you want further info, the community will be better equipped to help you if you provided your city and the car model/ year/ condition you are trying to purchase.