The Sprite? Nice idea. Though which model are you thinking of starting off with, the Mk1 or later ones? The MkI is the familiar "bug eye"...
And the MkII onwards had a more conventional (and
possibly more aerodynamic) look:
With regard to removing weight, I'd think you'd struggle given how light the cars are in the first place and how they aren't really filled with all the stuff that weighs down modern cars, like electrical equipment, thick carpets and insulation, power-everything, safety equipment... the only way you'd realistically save weight is by dumping the passenger seat, removing all carpets and most of the interior trim, and doing the extreme by replacing all the metal panels with glassfibre, polycarbonate or something similar. Which would also be expensive.
You could probably make aerodynamic improvements by removing the chrome bumpers and wing-mirrors and maybe making a rudimentary flat floor under the car, as older cars aren't known for their ground-hugging stance.
Lastly, what diesel engine are you planning on running? If you wanted a big project something like an engine transplant from a smart fortwo CDI would be entertaining.