If you are concerned that the trailer might be too hard to tow consider this. Shortening the trailer shell and frame might lighten it by 500 pounds which is negligible. The reduction in air drag will be practically nothing. So it will not make a significant difference to the ability of your car to tow it.
What will make a difference is what you add. Today's trailers weight at least twice as much, for the same length. But today's trailers are much more elaborately equipped.
If you rebuild your 1956
as it was originally, and resist the urge to add big water tanks, holding tanks, marble counter tops etc. it should tow just fine. Think of it as building an airplane where every ounce of weight counts.