As I noted in the answer to jurisdiction question, this issue should not be as contradictory as the question implies.
The Wizarding community would presumably inform the refusing wizard about consequences of violating the Statute of Secrecy and other laws about magic and Muggles.
Then, since at that age the wizard presumable can control their magic (not skillfully, but the won't make people blow up by accident), so they will be under a (explained to them beforehand) punishment should they violate the laws.
To be more precise, a " faint ability to cause magical maladies" wizard will do one of the following:
NOT cause " faint ability to cause magical maladies" because he won't use magic
OR, "cause magical maladies", and be arrested and/or punished as per Wizarding laws, and accident reversal squad or St Mungos will try and fix what they broke.
Simple as that.
A muggle equivalent would be driving a car. You can have a completely untrained driver behind the wheel. But if they cause an accident, they get punished, and an extra for driving without a license.