You have a much higher end camera than I do, so you'll be shopping for a release I probably wouldn't consider, and can't really speak to.
(Edit in: Wow! I think I'd get lost with that thing!
Impact 16-80)
But wireless is the way to go. You can sit back, or sit in the house, and run the camera. I've done that when starting a time lapse run in the wee hours of the night.
(I could use the delay start, but prefer to make sure the run is started.)
So get something that suits you and will work flawlessly with your Nikon 810 camera. You are headed on a great journey, choose wisely as you proceed.
Now then, last night I had some good skies and as is usual for me I was out playing. While waiting for my deep space equipment to suck down images of places we will never see in person, I was looking up at the waxing crescent of the Moon, thought about you and CathyAnn, and got my camera, tripod, and my 55-200 mm lens and my 150-600 mm Tamron lens. Time to get to work...
I tried the 200 mm, but it seemed woefully lacking in magnification to me. So I switched over to the Big Tammy, manual mode for either, and manual focus.
Since I'm a bottom dweller, I'm somewhat limited in my options in my camera. But I have picked up a few things in the 60K+ images I've shot with it since 2014 when I jumped in the river. I wanted to get back to some basics, to be a beginner again, but with a quiver full of arrows.
Shoot, look, adjust. Shoot, look, adjust. Shoot, look, adjust. I was using manual release, not a remote.
At 200 mm, I couldn't even find focus. So I gave up on that endeavor and changed over lenses. I wanted to try and get to your suggested 1 second at 600 mm.
Way too bright, way over exposed. (ISO 100)
I jumped down into the fractions, and continued my hunt, refining focus as I went. 1/4s, 1/125th, 1/160s, 1/200th, ... down to 1/400th.
At 1/200th the Moon still had a yellow cast to it for me. At 1/250th, it went to a blueish cast (image 3). I was hot on the trail hunting down a good exposure.... and trying to refine my focus as I went along by using Live View, and zooming in to get a more magnified view of my focus. Still shooting manual release...
So I wanted to share with you, and CathyAnn, how you could step into the exposure, slow to faster, until you find works best for your camera, your location, and your choices. I took 17 images between 8:49 PM (20:49) and 9:13 PM (21:13). If a turd like me on the bottom can do it, surely you can both too, and enjoy "Shootin the Moon", too.
Practice, practice, practice... and enjoy! (Untouched, as shot images.)