Hiring managers get a little bored at hearing elevator speeches in elevators or restrooms so I recommend the non-elevator speech. Rewrite your pitch so it doesn't sound like a pitch. Here is an example that I used when I was seeking a position as a writer:
“Hi, my name is Monte. I'm sorry. I guess you thought I was going to give you an elevator pitch. No, I wouldn't do that. I just here to mingle and relax. I could though. I mean, I'm a writer so I could write an elevator pitch if I wanted to. I have good presentation skills so I'm sure I could recite the pitch perfectly. After all, I have published several e-books and a few novels. I find writing is a good way to utilize my Masters Degree and vast experience. I could even write it with others since I'm such a good team player. I won't bore you with all the details of my work history or the numerous articles I have written for magazines. Unless, of course, you're interested. Another time perhaps. Here is my card. Oh, I've attached my resume to it in case you're hiring. Bye.”
I should warn you that I never got hired. Go figure.