Here are some opening lines that I used. Feel free to adapt them to your own needs. You can just fill in the blanks.
"Hi my name is ___ I'm looking for a job god help me please oh god help"
"Hi my name is ___ and I'm looking to expand my network. Will you be my friend?"
"Hi my name is ___ and I'm a recent graduate of ___. I notice you went there too. So you know that it's really shit, but you also know that we can both do this work. Please call me at ___."
"Hi my name is ___ and I'm looking for a job. Oh, you're just a 1-person shop? Okay, let me tell you about something I noticed on your website. You say that the name of your company is a 'play-on-words', but it's more specifically a portmanteau. Like how smog is smoke + fog, or how you take Clarkson + software to make Clarkware- Hello? Hello?"
"Hi my name is ___ and I'm trying to get into the ___ field. Do you have a problem with people with scary-looking beards? I just want to make sure you don't discriminate against beards before we go any farther." (Even if you do not yourself have a beard, this is still a good script because everybody should love beards.)
"Hi my name is ___ and my classmate ___ works at your firm. I helped him/her on an assignment once, so he/she owes me and should put in a good word for me. I need a job, too. When can I start?"
"Hi my name is ___ and I need to pretend to be employed so I can get the line of credit I need to finance a big cash deal tonight. Could I trouble you to verify that I'm a VP there and make $200K? Thanks very much."