This post was suggested by an emailer named Darell.
I have talked previously about the terrific Gold Key series, Magnus, Robot Fighter. In the back of each of the Magnus comics was a four-page serial called The Aliens. The series started with the contact with Earthmen:
First Contact, by Murray Leinster. The dilemma was resolved by having the two species swap ships after wiping out all information that could identify their home planets. However, that wouldn't make for much of a serial, so in The Aliens, the solution is:
Over the next several issues, we see the aliens and the Earthmen developing a bond and trust for each other as they help the other species out of difficulties:
Captain Johner and the Aliens.