EU Citizen moving to Sweden with non-EU wife while working remotely for non-EU/Swedish company

I'm a German citizen that wants to move to Sweden with my South African wife. We've been married for almost two decades and both still work for a South African based company, in fact my wife owns the company we work for. The plan is to work remotely while in Sweden.

What is the best way of going about this? I will not be earning in Sweden but we will have enough funds to sustain ourselves.

Is it best to go the Right of Residence route? What paperwork would be required from us?

Thank you :)