Well I have looked at this from multiple angles and I just do not see a way of putting fins on a tear without a major reworking of the shape and functionality. I have put some fins on odd things too, I put a set of 59 Cadillac fins on my 1966 Ranchero.
The only way you could make this look right is to give the whole thing a longer, lower body. More like a car or a boat. To keep the tear functional you may want to look in to fooling the eye with a clever paint scheme which mimics the lines you would get on a car with fins.
I forget which one it is offhand but there was a trailer that had some little "Buck Rogers" type fins attached to the side.
You may even want to go for that boat design. Cheange the shape of the front and have a forward slung, enclosed cabin.