There is nothing wrong with taking loans that do not involve paying any interest.
If your wife takes a loan, she may give it to you by way of a loan, or as a gift or partnership. But if she takes a loan in order to work on a specific project, then she has to fulfil that, because the Prophet (blessings and peace of Allah be upon him) said: “The Muslims are bound by their conditions.” Narrated by Abu Dawood (3594); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
It is no secret that it is not permissible to lie, deceive or use tricks; rather it is obligatory to adhere to the terms of the contract between your wife and the lender.
And Allah knows best.