Well, the best thing is of course to just be out with it completely without holding back. Then your sin can't hurt you anymore.
However, if the "human" aspect of confession is really bothering you, perhaps try thinking of a way to phrase it that's not so specific. That's what my nouna said when I was biting my fingernails off about first confession. If this sounds weird or wrong to some of you, let me explain something: my church's priest and my confessor is my friend's dad.

If I were to sin in some way involving my friend, how am I supposed to confess that? It's the sin itself that I need help with, so what's the need for all the specifics? I don't really have anyplace else I could go to for confession. And if I were to sin WITH my friend (hypothetically, nobody get any ideas!

"Your son and I knocked over a liquor store last week!"), that too would bring up a "conflict of interest", so to speak, if I were to name names, as it should be up to my friend to confess the sin on his own to his own confessor. So there you go.
However, I have to stress again, it is best to be completely open with your confessor so that you can be sure to get whatever help you need and expel this sin and the guilt it causes from your life.
One more thing--another thing you might try is just blurting it out really fast. Christ can understand you no matter how fast you're speaking and it'll be over in an instant. That's what I do whenever I have bad news or something else unpleasant that I have to tell someone.