Just some thoughts, Show Dog lines may or may not have the desired traits. Even dogs of a particular breed often have the same tendencies, but may vary noticeably from individual Dogs and/or lines. There is a difference between a breed and a line. Example, car, Chevrolet, Camero, now the next question is, what does it have under the hood? They may all look the same, but the differences can be major.
Two schools of thought. One is to get a smart Dog and train it to hunt what you want it to hunt. Or get a Dog with a strong prey drive and try to coax it to hunt what you want.
Many of the show Dog types that you mentioned have been bred for appearance, more than hunting prowess.
Some Dogs you may not associate with Squirrel hunting may be really good at it. The best Squirrel Dog I ever had was a full blooded German Sheppard. He hated Squirrels and I could control him.
The one with the most potential was a Plummer Terrier. But it's prey drive was almost too strong, They are often strong willed and hard to control. They can take prolonged training and a lot of patience, even then the results may be iffy. My Plummers can be like an unguided missile. You may want to hunt Squirrels, they may want to hunt Rabbits, Ground Hogs, Fox or whatever. And once they get a prey in their sites (eyes or nose), good luck getting them to change direction. Even Dogs from the same litter can have different strengths and weaknesses. I have one Plummer that loves tight places and will head underground as a preference. And another that doesn't mind tight places, but is more inclined to find something to kill, anything, anywhere, anytime. He'll tear a Squirrel to bites faster than you can say stop. My earth Dog is more likely to latch on and hold on rather than tear whatever to pieces. Same Breed, same litter, two personalities.