My wife is Chinese. Can I get a resident visa without applying for a work permit?

Yes, you can apply for a one year family visa/ a residence permit with same duration in China. So, better apply for a tourist visa to enter China first. However, you are not allowed to work on this visaresidence permit. You can refer to https://www.travelchinaguide.com/embassy/visa/family-visit-permit.htm if you need more details.