This seems like a question for a psychologist, not a wildlife biologist! It's not unwise to be cautious around spiders because some of them can hurt or even kill you! I would say that you never even need to get comfortable holding spiders, because spiders certainly don't enjoy being held! I think the trick is just to learn that the vast majority of spiders can do you no harm at all and the chances of being bitten by a dangerous one are very, very small. Spiders don't chase or attack people. Leave them alone and they'll leave you alone. This applies as well to snakes, bees, and lots of other animals of which people are irrationally afraid. Conquering these irrational fears is the key. But again, that's a job for a psychologist.
Your fear of spiders sounds as if it might be a little too mild to be considered arachnophobia, but if you type that word into a Web browser, you'll find several companies that offer products and services to cure it and other phobias. A phobia is "an abnormal intense and irrational fear of a given situation, organism, or object."
By the way, the word is "skittish," not "skidish."