By not hurting the walls, do you mean the Zolatone beneath the paint or the aluminum?
You can strip both the paint & Zolatone using the same products as the clearcoat on the exterior...if you are going to try to just strip the paint and hope to revive the Zolatone underneath, I doubt that would be very sucessful. If the paint is adhered well, and you want to get it back to "original" I would re-Zolatone over it, otherwise, strip it all off then re-Zolatone.
Kleen Strip, Bix, Citri-Strip are some of the products used for stripping...if you perform a "search" using stripper as a keyword, there will be other products that come up ~
P.S. Congrats on the '64 GT...a great trailer, I hope you get as much enjoyment out of ours as we have ours.