Everything would have been redesigned from the ground up. Where TOS was ostensibly 60's, I would have taken a 1950's influence. The Enterprise would have resembled a 1950's rocket ship, there would be flying saucers and big bug-eyed aliens and sentient blobs in space.
I would do away with all the boring stuff (ie. UFP, Starfleet, politics etc) and focus primarily on a ship in the middle of nowhere encountering weird stuff. It would be lighter in tone and made more accessible by abandoning any season long story-arcs. I would embrace the reset button but not in regards to character evolution.
Tonally, it would be similar to nu-Doctor Who, Sherlock, Firely etc. Smart scripts and stories not afraid to take risks.
I'd keep Scott Bakula as he was the only cast member with any on screen chemistry with those around him.
It would be a spectacular failure of course, but would hopefully be remembered fondly.