Loads of factors in play that will affect pattern. Choke is just one of them. Cartridge choice is another. Shot "should" be spherical, and fly in a fairly straight direction. Damage to the shot cause it to fly in different directions. More damage to the shot equals bigger pattern.
Just some of the factors:
For the same size shot, recent/pricier cartridges with 5% antimony deform less than older/cheaper cartridges with softer shot ( 0 % or 2%), so give a tighter pattern. Steel shot hardly deforms at all, so gives an even tighter pattern.
The same hardness shot will pattern differently depending upon shot size. Smaller shot receives more damage as a percentage of its surface area, therefore bigger pattern. Also the higher pellet count in 28g of smaller shot gives more opportunity collisions of shot. Hence why there’s also discussions on whether a 24g 7-1/2 patterns better than a 28g 7-1/2. When you start talking 9’s, then even the amount the shot heats up when travelling down the barrel affects the malleability, which is why some shot is plated with nickel or copper.
Plastic wad will pattern tighter than fibre, as the shot is mostly in the shot cup when travelling down the barrel, and not scraping the bore causing more damage.
Choke forces a tighter pattern, but at a cost. It causes a radial pressure on the shot, which tightens the pattern, but as a result causes more deformation to the shot as it’s now all trying to get through a smaller bore at the same time. Fortunately the effects of the pattern constriction are greater than the extra spread due to deformation of the shot.
So yes, choke does have a part to play. But not as much as it did years ago, when cartridges were crap.
And of course that's your choice, I would use the same cartridge size and open up the chokes
Thus decreasing pattern density, and potentially allowing a big enough gap for a clay to pass through?