Let's assume a reentry craft designed to not use heat protection like Soyuz or the Space Shuttle, and budget is not an issue. The Concorde max surface temperature was 400 K, so let's use this as a max temperature for our craft as well.
Let's also assume that size and shape of the orbiting craft is no problem, though mass still is. It can have inflatable or unfolding aerogel wings like an atmospheric satellite, or some other technique, in order to have a wingspan as wide as necessary without adding too much mass.
The craft is designed to spend as much time as possible in the extreme high atmosphere, in order to slow down at a rate low enough that heat load can be dealt with simply by radiating it away (I doubt ambient air would be much good to carry heat away at those altitudes and speeds). As such, as it is slowing down, it must use lift for staying high enough, and use control surfaces for attitude control if possible.
Ideally, it would slow down to low supersonic or even subsonic speed before reaching a part of the atmosphere where heating is a problem, then fly like a plane or a glider. If possible, let's ignore what exactly happens after that point.
What characteristics would such a craft need? What lift-to-drag ratio, radiative surface area and general shape would it have? What would be its flight path?
I hesitated between here and Aviation SE, but there are already related questions here:
Gliding into the atmosphere is more about attempting it with a Cessna instead of a purpose-built craft.
Challenging Karman line from above is leaving aside the question of heat, with a hypothetically heat-resistant glider
Can a reentry be done slowly? is a more general question about shallower reentry