Is expiation obligatory upon one who swore to listen to a recording, intending to listen only to the permissible part of it, but then listened to another part that he feared might be unlawful?

If you do what you swore to do, then there is no expiation upon you. If your intention was to listen to a part of the recording, then your words can bear that intention, and you are absolved by listening to the part you intended.