Managers are not and should not be the only people who are doing the work to maintain and run a shop department. Their role is just as much about making sure things get done as it is about pitching in and getting things done themselves.
Shop managers should absolutely recruit members to help them with tasks around the shop.
A good place to start is the people that are very active in your department, people that are using the area a lot are invested in the area staying up, running, and efficient.
There are several approaches on this and it is honestly going to depend on what the tasks are and who you are approaching for the help.
Here are some general ways most managers engage the community for help:
Really anything and everything you need help with: