I didn't know you could get a cap just to smoke in.
All the years I smoked and I never possessed a smoking jacket or a smoking cap.
I once read that the upper class/gentry weren't smoking tobacco but opium, either pure or mixed with tobacco, when wearing smoking hats and jackets. They were worn to smoke the stuff then almost pass out, hence the comfy clothing to make it a more pleasurable experience, rather than smoking opium in stiff formal clothing. My dad who did his national service mainly in Hong Kong told me about opium dens where servicemen got high on opium. He mentioned them taking off their uniforms and wearing Chinese silk dressing gowns, similar to a smoking jacket.
In short, the upper classes didn't don a smoking jacket and hat every time they fancied a quick Woodbine out the back door.