Definite no. You would regret doing that because it'll beat the car up pretty bad.
I'd recommend a combo of the above mentioned..
A. buy a Serp express or build your own version
B. Tape the path of a toneau and use that along with a road guard on the front of the trailer. Your tow vehicle will kick alot of debris up onto the trailer!
For a trailer, if you only plan to haul your cobra and nothing bigger, I like this
Big Tex Equipment Trailers; Trailers For Less
I've got one like this but a in steel and it's a 20+2 footer. I haul much bigger cars! haha But this front shiled would probably cover the entire cobra, it's about 4' tall
But combine that with a tonneau and I think you get the best of both worlds.