I will stop at "identify" such people, at the least to have treatment available to them. There's no need to "apprehend" until you know a crime has been committed.
And I don't agree with capital punishment for the most part (innocent people can sometimes be executed, which is the main reason capital punishment is in invalid, not because an actually guilty person does not deserve it). To the degree I agree with capital punishment is for cases where the guilty are committing acts that are existentially detrimental to most inhabitants of this planet or a large group of people. Genocide and destroying the climate to make the planet uninhabitable are existential threats to a lot of people. While pedophilia sucks, its effects are limited to a smaller number of victims, and once caught the person can be kept imprisoned permanently if necessary to prevent further attacks.
Now as for pedophiles who have not yet been born, and the science was foolproof in detecting them with a 100% accuracy rate over a long period of time, then potentially adjusting them before birth or terminating the pregnancy ... or just completely weeding the flaw out of human DNA prior to any conception at all or preventing the conception, that would fine by me, whether you call it "eugenics" or not.
