There's a filter to delay the video, but nothing to delay the audio. I actually needed that yesterday, and didn't find it.
There's the Sync Offset in the Advanced Audio Properties, but that applies directly to the encoder, so the Monitor (which I really needed) is unaffected, and it only cares about sources, not scenes. If you only need it in the stream or recording, and if the source that needs it is part of a scene (not global), then it can work as you describe.
Set it by trial-and-error, and maybe some measurement in your favorite video editor (not OBS) that can process the picture and sound separately.
