First of all, most likely your Mossberg does not have "no choke," unless you mean you are using a cylinder choke tube or no choke tube. In the latter case, you have probably ruined the barrel.
I rarely use Modified for squirrels, and then only in the very early season with lots of leaves on the trees and expected closer running shots.
I use Improved Modified in the first part of the season when there are still leaves on the trees but I can get shots farther out.
I prefer Full in late season with no leaves on the trees.
I use #5 lead shot exclusively in 20 ga. and larger guns. #6 in smaller bores. I'd use full choke exclusively in the .410.
More choke will "mess up" your squirrel more, not less, as it theoretically puts more pellets in the target.
U.S. Choke % of pellets in 30" circle @ 40 yards
Cylinder <45
Imp. Cyl. 45-55
Modified 55-65
Imp. Mod. 65-70
Full 70-80
X Full >80
The above does not apply to .410 bore.
There are other chokes besides and between these.