I believe 1 Corinthians is correctional rather than instructional in its intent.
In chapter 15 Paul is correcting their failure to understand the Resurrection. He states in verse 3 the Gospel he preached to them, making sure to include the Resurrection. But it seems clear to me that the "our" refers to the people of Corinth assembled together in that local church, not the entire population at large.
As his remarks are correctional of the Corinthian Church, I don't see them as instructional as to what they should be preaching to the lost, but rather correctional as to what they themselves believed.
He brings his primary intent into focus in verse 12 when he says "how can some of you say there is no Resurrection?"
His use of the word "our" as being limited to believers here seems, in my opinion, to parallel his remarks in Romans 4:25 where he makes a similar statement when he says "Who was delivered for our offences, and was raised again for our justification."
If the "our" there is all inclusive, all people everywhere, without exception, rather than just referring to believers then are all people everywhere justified, as he does say He was raised again for "our" justification?