Are you going to sell your home? If not or if you own any residence, you may be a risk of having NY State come after you for income taxes.
Otherwise you should have no issues. When we left NY as full timers we had already sold our house. In advance I set up a mailing service in South Dakota and transferred our bank address to the South Dakota address including having new checks printed. Make address changes with all financial institutions and with anyone who sends you mail. Once you physically leave NY, you will need to stop in South Dakota or other State of your choosing for at least one night. A receipt for the stay should include both you and your spouses names. That receipt and a bank statement with your new address will be all you need to set up new vehicle insurance and to register with DMV. I also recommend submitting IRS Change of Address Form 8822. Although not absolutely necessary it is another verification of your change of address from NY to SD.
I have only one caveat on the change of address. Some banks and other mainly financial institutions want an "actual" address. Your mail forwarding address will include a PMB (Personal Mailbox) number. Avoid any concerns by dropping the "PMB" designation. Just include the number as if it was an apartment number. I would not lie about this, just avoid making an issue when not needed.
There should be no "winging" involved and nothing to be caught about unless you maintain residential property in NY. You will be a resident of SD, or another State of your choosing. Your voting registration will also be in SD, not NY. Same with insurance, both vehicle and medical. I have heard medical can be an issue. We had no problems maintaining prior coverage with just an address change.