It n Ed’s to heal by secondary intention- the skin cells need to grow in from the sides to cover the wound. In the past the advice was to leave it to scab and dry out. But more up to date thinking now realises that keeping the wound moist allows the cells to move rapidly through the granulation tissue ( firmed when the blood clot organises in the early stages of healing). If the wound drys out it’s much harder for new cells to migrate.
If you consider the way other animals deal with cuts they constantly lick the wound. The saliva contains antibodies and other antibacterial components speeding up healing. Recent research comparing healing in the mouth compared with the skin ( almost identical in healing behaviour) shows that mouths heal 10x faster because the wound doesn’t dry out and is bathed/irrigated continuously with saliva.
So for a wound like OP’s the best thing to use is a dressing that seals the wound keeping it moist, something like Tegaderm.
My son managed to cut his hand open a couple of years ago, had an altercation with a glass panel in our front door. It was a deep clean wound but the incompetent junior doctor in A&E made a mess of the suturing and the wound opened up after the sutures were removed. It would have taken weeks to heal if left open and the urge to pick the scab fit a teenage boy too much. He was also flying out to India the day the stitches were removed. He took a box of Tegaderm with him and sent a photo to me every day so I could keep an eye on it. It’s now a standby no joke that his photographic record of his trip to India included a shot of his hand in every photo.
It heal d without incident although did need antibiotics when it looked a bit dodgy after swimming in a hotel pool ( despite being instructed not to)
Allowing a scab to firm on the knuckle will just lead to it cracking and bleeding, keeping the wound moist will make using your thumb easier.
Sorry for the length of the post but as a HCP I like to backup suggestions and give easy to understand examples/experience.
I also took the tip of my finger off with a mandolin last year and had to apply the same method. I now have a special pair of chain mail gloves for using the mandolin, and any other lethal gadget in the kitchen. I’m a bit prone to slick no bits off my hands.