It won’t be much of a ding. 5-10 points for a couple of months.
As for sales tax - most likely (if it’s similar to my state) - Nissan should send you title and you go with it to DMV to register at which point DMV will ask for taxes.
The funny part in all of this - payoff letters used to include sales taxes to confuse consumers because it was always higher than dealer payoff but it would never show as separate number.
Leveraging useful financial products at favorable terms is what your credit is for. 
The actual impact is going to depend a lot on what the rest of your profile looks like, but with a clean, seasoned credit file you may not even notice.
I had a new auto loan report last month.
The pay off amount from your 2 options should be different. Financial institution option has tax
Not sure if the 800lb animal in the room has been addressed: why are you buying a used Nissan? They seem to be turning around with the 2021 and newer models but for a long time Nissans were cheap junk that were only good for cheap leases. They won’t hold up. They won’t hold their value. Why on earth would you purchase a 2018 or 2019 Nissan product?
It’s in your lease contract. You have a right to purchase the car at the end of the lease that’s written into the lease.
I would call and request payoff letter.
Not sure about Nissan specific, but here’s the info for Infiniti from payoff letter.
I have requested a payoff letter via my Nissan Finance portal - and they have two (dealer-assisted or financial institution).
They amount - always excl. taxes - they list there is the same for both.
My dealer likes to have that amount +$75 Nissan fee + $300 buy fee + taxes 
Not sure about $75 Nissan fee, but ‘$300 buy fee + taxes’ is irrespective of dealer assisted buy or direct payment to NISC. If your dealer is not charging anything else, then it might be smooth path as they can include taxes in final amount rather than you visiting DMV later if paying directly to NISC.
The dealer is going to perform Registration for you, so they will collect the taxes.
If you buy out (indirectly via bank) when you go to the DMV to register the car in your name, they will ask you for the taxes on the purchase price. Either way the government gets their tax money.
You can buy or sell leased Hyundai without the dealer. Not sure why it is on Your list.
I was talking in general about degrees of shadiness across various brands’ dealer networks. 
Two of my favorite Toyota experiences were when a sales guy told us that Toyota.com was wrong and they don’t actually manufacture the color combo we configured on the site (guess what, they didn’t have any like that in stock), and at another Toyota location a sales manager shoved an “invoice” under our nose and then pretended not to know what “TDA” stood for when I asked (it’s an advertising fee; "Toyota Dealer Advertising, or something like that).
I hadn’t even asked to see the invoice, because I know that’s not a valid reference point anyway.
