I haven't played with delay, but I have used a Lua script to set the volume of an audio source via obs_source_set_volume.
The docs show functions available for sync offset:
void obs_source_set_sync_offset(
obs_source_t *source, int64_t
offset)
int64_t obs_source_get_sync_offset(const
obs_source_t *source)
Sets/gets the audio sync offset (in nanoseconds) for a (audio) source.
So you COULD have hotkey action in the script.
But the nicest solution would be to have the script automatically set the sync value based on which video source is currently in use.
The script could register for the source_activate signal. If the activated source is one of your video sources, it would set the appropriate sync delay in the audio source.