I've never run over a squirrel before but I have almost crashed a few times. Once I almost lost control over a side of the trail that rolls down about 5-7 meters through what I saw was garbage, glass, and brush into a river/creek.
So many times as many people have said these little critters run out at literally the last second that you almost can not avoid them. I've run over many a road kill before but they are already dead before I got there and often traffic around did not give me enough room to evade. I feel bad but at the same time I hope they did not suffer and passed on quickly.
If this helps, if you're able to spot the squirrel a little bits away or as you're coming close see if you can lift the front of your wheel in a slight lift but not pull a wheelie. Like jumping a curb/pothole lift is what I'm taking about. I find that many a squirells see you moving up and down and they end to run away then, then in front of you.
Another tip someone told me before (pending if you have pockets) is to pick up a few small pebbles and keep in the pocket. As you approach the squirrel on the road/trail that is on the path throw a pebble down range. Yes by-passers by may think evil of you but you know you're just startling the squirrel away as you're faster then they are. Hey who knows, you might get a headshot for 100 points.
If you do get consistant headshots then you might want go to the carnie games more often and clean house for the stuffed prizes!
On a side note, reminds me of the time I got kicked out from playing a carnie game that you fish for the red magnetic puck in a sea of yellow pucks in running water. You always win a prize there if you get the yellow which was some stuffed snake. A red puck won you a mid-size prize. The prize system was 3 snakes trades up to one mid-size stuffed prize. If you have 3 mid-sized prizes you can trade up for 1 large stuffed prize. It was something like $5 for two tries if I recall right. I got a family of wolves, some snakes (which I call wolf food
), a large wolf, and a large aligator. Not bad when I think about it. I think I had the winning hand then as mid-sized prizes probably costed them ~$1.50-$2/unit and large prizes $5/unit so they wanted more people to win the ~$0.50 cent snakes to make more money.