I need a 1 month work visa but would like to travel for period of time afterwards.

1 month work Z?
You mean you only need to work one month in China?
If you only work one month, you are suggested to consult with your company to extend your staying in China a bit longer. With their approval, you can apply for a residence permit with a long period, so that you can travel through China during the validity of your residence permit.

Usually, foreingers are required to change their Work Z into a residence permit within 30 days after they enter China. Then with the residence permit, they can live in China for a long time till they finish their work.