CAN SPAM legalities aside, have you thought about just going to some local businesses, offering them a copy and asking for their support? Have you considered creating a mock up with how their ad would look in your publication and sending that to them?
Technically, under CAN SPAM you can send them an email as long as your subject line is not misleading, you have a physical contact address info and you include a working unsubscribe link.
Yes, you can do that, but why would you? What's the incentive for me to sign up with your publication? Think of it this way, when you go advertising for new sponsors, don't you think they'll be judging what you may be able to do for them based on how you solicit their business? I mean, if you can't get their attention, how will you get other's attention for them?