Good luck with your book,
Since it is a cash purchase, the shortest period will depend on the attorneys representing the buyer and the seller, if this practice is customary in your state wherein each party is represented by his own closing attorney.
Another consideration would be the home inspection contingency date. In Connecticut, the contingency date can take within 10 to 14 days from the date of the fully-executed contract.
The local professionals who will be involved in the transaction can best answer your question. My response is just to give you an idea.
Mary Jo Posterli