How do you pay a working owner weekly without running them through payroll.

if the owner's company is a sole proprietor or partnership, then he can be paid whenever he wants as an equity draw.  Write a check, hand him cash, however you want to do it

If you company is  subvhapter S corporation the working owner MUST be on payroll for what the IRS considers reasonable wage.

Any other non corporate entity the owner is not paid but receives withdrawal of equity in advance of end of year pass through profits.

All the money in the business is at the disposal of the owner. You should have a minimum of 3 equity accounts for each owner. Equity, Contributios, Draw. Better is to make all three sub accounts of a parent summing account. "Pay" the owner against the Draw account. Whatever cash the owner contributes or business costs paid personally go against Contributions.

End of year profit or loss first to retained earnings and then to Equity and on day 1 of new year zero out Contributions and Draw by rolling up into Equity