If you wish to fly within the Class B or C airspace, then you are required to have the transponder whether or not you have electrical, single seater or no.
Lack of electrical system excuses you from needing to have a transponder within the 30-mile Class B "Veil", as long as you stay out of the actual Class B airspace (inverted wedding cake). Again, doesn't matter how many seats the plane has.
A single seater *is* excused from the ELT requirement.
Ron Wanttaja