As an executor of a will can one use quit claim deeds to execute the will without hiring a lawyer? The only things left in the will to be transferred to other names is some mineral rights and grave plots.

I doubt I can answer the "quit claim" question but as executor you know that you are charged with the responsibility of gathering estate assets, managing estate assets, and then dispersing estate assets to the heirs as per the will. If the estate consists of real estate, just be sure to follow the terms of the will whatever they maybe. Perhaps a real estate attorney or other expert trained in or experience with real estate mattes can answer.