Christian Health Share

The expense account and how the deduction appears, or does not appear, on the W-2 are two different things.

If you're tracking this as an employee deduction on the employee paychecks, and you don't want it to appear on the W-2, then edit the payroll item and choose "None" as the tax tracking type. Also in this case, the account to use shouldn't be an expense accounts, because employee deductions are not expenses to you. Instead, they are a liability, because you must remit the money you've taken from the employee to the Health Share plan/company.  You could use a specific liability account just for this case.

That noted, I googled "health share plan" and got:

"Health share plans are member-based organizations, often faith-based, where individuals with common beliefs contribute monthly to a shared pool to cover each other's medical costs. They are not insurance, offer no guarantees of payment, and are ideal for healthy individuals looking for lower-cost, catastrophic coverage."

Based on that, I'd say run, run away and go back to actual insurance.