Withdrawing paper from a conference after presentation due to error
You are overthinking it. A simple note is all you really need. "The paper needs to be withdrawn as we have found a serious error that we don't believe can be corrected in time for the conference." 

This won't have been the first time that a paper has been withdrawn. It is a matter of scheduling sessions for the program committee but some of the members are probably familiar with that. There may be some scrambling, however, if proceedings have already gone to press. But they should have copyrights in order before that happens. If they don't, then it is their problem, not yours. 

No, you don't need to detail the error, just that it exists and that you don't have a ready fix. If the conference is part of a continuing series you may have it ready by next year (or whenever).