Callous as it may sound, a rat trap baited with peanut butter is good for red squirrels. Don't know about the grays. Rat poison would probably work.
My dog does a good job of keeping them at a bare minimum around our place. One thing you may want to keep in mind about squirrels and wanting to spare their lives... Squirrels love to overwinter in your house! They will find or make an opening in the eaves and take up residence in your attic or air space under the roof. They will then gnaw on wires which can cause electrical fires. Yes they may be cute but they are a royal PITA not to mention destructive if they decide to make your house their home instead of the trees. Also they will bring in fleas. I am a big animal lover but when it comes to destructive vermine and my house I will take advantage of any technology to kill them.