Operating a Delaware Corp without having issued shares

Non-issuance of shares poses no problem whatsoever indefinitely as long you are the sole controlling director and officer and no shares are issued to anyone else.
I strongly recommend against backdating any document. Using a backdated document for an improper purpose can be a civil fraud and a criminal offense. For example, the SEC years ago cracked down on backdating of stock options to establish a lower exercise price. In some situations involving private matters such as commercial contracts, it may be appropriate and justified to establish a retroactive effective date, which is quite different. This practice has an effect only between the parties, not third parties, and should be implemented by stating that the contract has taken effect "As of ________" (the retroactive date). One example is where two parties agree orally on June 13, 2016 to exchange confidential information beginning that day subject to a written non-disclosure agreement, which is not prepared and signed until June 17. The agreement should provide, " This Non-Disclosure Agreement is entered into as of June 13, 2016 ...". In this case info exchanged June 13-16 is equally covered and the practice is recognized as fully valid and legitimate.