I have used 4 methods for splatter ( dots, not "webbing)
For touch-up :
Tooth brush ( too much effort for me to do an entire cabinet )
For entire cabinet:
Rattle can:Drill the spray hole in the nozzle a touch larger. Prevents the hole from fully atomizing paint.
Rattle can: Use the partial push down method. Again prevents the paint from being fully atomized.
With some practice the entire cabinet can be done in 15 minutes.
In trying to duplicate the multicolor paint schemes on a 1950s game (dots on dots)
I bought a HF popcorn drywall air gun. Used the smallest nozzle and loaded raw latex paint.
I was able to layer on top of a base coat rolled onto the cabinet with fabulous results.
All of the above require practice on something other than the game to find proper angles, distances and air pressures.
I used cardboard to figure all these out. In the case of the HF popcorn gun. I made a tape parameter around the game so I knew exactly how close to get.
This is going to be messy. Cover everything and avoid spraying near the wife's Maserati. Wear eye protection and old clothes. Tarp the floor and anything of value.
As pointed out above, it is easy to go overboard. Take some before picks. There is not as much on there as you think. (Speaking from personal experience)