As CheerMum says, there are lots of options. There is also an option of doing none, or fewer than is normal in schools, or doing them earlier, or doing some early and more later. Or almost anything really!
DS was only out of school for the GCSE years, and he did IGCSEs through an online school. But that's about the most "school-like" option there is, and plenty of people choose to do them by working through textbooks and other materials.
One of the tricky things about explaining HE to family and friends is that they start from an expectation of what school is like, and want to know how you will replicate that. When the point for most people is not to replicate school but to be more flexible. But when your answer is "anything or nothing or somewhere in between" they struggle to understand how you can be vague about something so important.
If you do go with GCSEs, your DC can study independently, or with a tutor, or with an online tutor, or a distance learning company, or an online school, or an FE college, depending on what suits them really. Apart from the FE college one, its easier for them to do IGCSEs as they can be done without having to get coursework marked.