Just to ease your mind, I have towed a Scamp
13 over 600 miles with no interior cabinets. While it acted somewhat like a pillar of Jello, it suffered no damage. When replacing or installing new interior components , care must be taken to maintain the shape of the shell and to providing adequate support and stiffness.
The trailer won't collapse under it's own weight
from simply removing the interior, but it may move around a little which requires a little care.
below are photos of "Shelly"(the afore mentioned Scamp
13) the first is the shell without furniture or support, the second and third are the finished trailer with a full interior....