You can actually use a bit of Twig logic to determine your category URI formats.
Try this for your Category URI Format:
{parent ? parent.uri : 'what-we-do'}/{slug}
Which is just a more compact way of doing this:
{% if parent %}{{ parent.uri }}{% else %}what-we-do{% endif %}/{slug}
That will only add 'what-we-do' to the URI if the current category doesn't have a parent (top-level category). Otherwise, it prepends the entire parent's URI.
That should give you URIs like:
/what-we-do/service-one
/what-we-do/service-one/subservice-one-a
/what-we-do/service-one/subservice-one-b
/what-we-do/service-one/subservice-one-b/subservice-one-b-nested