Do I have to lose to win?
Yes, it is possible to retire your Magikarp early. Though not as early as you're probably after.
If you click your trainer profile (the button showing your level and progress to the next trainer level), then scroll to the bottom, it has an item to retire the fish. But it's only active after you have trained a certain number of times.
I'm not sure whether you get the large number of points bonus for doing so the way you do for completing training entirely though.