Two things to note, first you may want to ensure it is not a female with young still in a nest before removing it (lethally or otherwise). Starvation is a shitty way to go. Second, transporting problem wildlife and releasing them in a different location should not be considered a viable solution. I could rant about the potential issues associated with that practice, but let's just agree to find an actual solution, not just move the problem.
Non-lethal options that work are limited, but the most likely to succeed is exclusion. Ensure the squirrel isn't in the space where you don't want it and put up material to keep it out. Take away as many of the reasons it wants to be there (shelter, food, water, etc.) as possible.
You can trap squirrels quite easily with home made or store bought traps. Pre-baiting will improve success. For example, with tuyops trap leave the cooler in place with peanuts inside but "unarmed", and allow the squirrel to find the nuts. It will get comfortable going into the cooler, figure out the peanuts are a tasty free meal and readily enter next time. Sometimes this can happen in a day, other times it may take a week or longer for them to figure it out. Once there is evidence of the squirrel taking the bait, arm the trap and catch yourself a squirrel. Alternatively, you can snare squirrels in their runs (e.g. along the top of fences). No bait required.
If you do end up going lethal, eat 'em! Squirrel is tasty. :)
