Is it ok to secretly marry a second wife if the laws of the country, like in many countries in the West, does not allow marrying more than one wife at a time?
We are not dealing here with legal matters nor giving any legal advice. We are dealing with Islamic matters and reflecting the rulings of the leading scholars ( Maraaji' of Taqleed). Muslim should not break the law of the country where he lives unless it contradicts with his faith and religion.
Main matter in second marriage is fulfilling the Islamic conditions of practical justice between wives. If this condition is not fulfilled, second marriage will be not permissible in Islam.
If your question is a legal question, you should ask your legal adviser.
Wassalam.