You have a duty to tell your opponent that you have incurred a penalty as soon as it is practical / possible to do so. If you are 50 yards apart you don’t need to shout across the course, but you may be able to pass the message using actions, or let them know as soon as you are close enough to speak (and you should move towards them if your paths are still diverging as you proceed down the hole).
Similarly to declaring your correct handicap you have a duty to tell your opponent the correct number of strokes you have taken whenever they ask. If you refuse to answer that is taken as an automatic incorrect answer. As declaring either too many strokes or too few strokes could both affect your opponents decision making on how they play their next stroke, you lose the hole if you tell them an incorrect number and do not correct it before they play their next stroke or take a similar action such as conceding a stroke or the hole.