White label dynamic branding for Connect Chat widget

I am working on a white-label applications that dynamically applies the branding for multiple clients. I want to add Amazon Connect chat widget on this website. Now I am aware I can set default branding on the widget but that will not work for all clients. I see I can set branding when initiating the chat widget in article Pass custom styles to override the defaults in the chat widget. Is there a way to dynamically change the branding at runtime?