Why do you want to get rid of them?
You can get over it. We renovated the house here and I cannot tell you how many close encounters with unpleasantly large spiders I've had in the last 5 or 6 years.Because I have arachnophobia and can't attend to my buns if there are spiders in the sheds.
Some people cannot get over spider phobias though, no matter how good they are at eating flies, they are just truly terrifying to some.
I know they're "safe around (non-insect) animals" but I'd worry about all the chemical residues - so I'd try the conker route first.it's meant for the housing area and hutches so i use about 2/3 tins when i do the whole shed but i only do it about twice a year. i spray a lot around the door edges and places they would get in.