Yes. Simply send the data in the clear.
Passive attacks are not possible. For a passive attack to work, the data must be intercepted by someone other than the intended recipient. But by your definition of "pre-shared information" the existence of an intended recipient would count as "pre-shared information" (since both sides would know this). So anyone who receives the traffic is just as much the recipient as anyone else.
Active attacks are not possible. Active attacks involve someone other than the person the other side expects to be sending the data to be able to influence the data or receive the data. Since neither side has any expectations as to who is originating or receiving the data (such an expectation would be "pre-shared information" since both sides would need to have it), such an attack cannot, by definition, exist.
The idea of a "secure channel" to nobody in particular simply isn't coherent. And if both sides knew who they wanted to speak to or hear from, that would be "pre-shared information" by your expansive definition.
So this is not a coherent thing to want.
Consider two people considering such a scheme, Alice and Bill. If Bill knows who Bill is, Alice cannot know who Bill is as that would be pre-shared information. If Alice knows who Alice is, then Bill cannot know who Alice is, as that would be pre-shared information. Thus Bill could not distinguish a secure link to Alice from a secure link to Fred. To Bill, either is just as good. So it matters not if Fred intercepts or distorts the data. Fred is no less the intended recipient.
Update: If literally all you know is the address, then nothing could provide any more security than simply sending to that address. Since the address is all you know, whoever can receive something sent to that address is the intended recipient, right? And it doesn't matter what that person receives, since you are no different from an attacker, they wouldn't care whether they received what you sent or what someone else sent -- they don't know who you are.
