Can I hire a part-time employee (20 hours per week) and pay the employee to spend part of their time doing charitable giving work?

Assuming that you have the approval of the business's owners (e.g. shareholders; under some circumstances you might owe a duty to the business's creditors as well) to make this charitable donation, I see no reason why not.  Many law firms hire associates and assign them to work, at least part of the time, on pro bono matters.