Look into a Stihl 4 mix. Its a 4 stroke that uses pre mix fuel but is a 4 stroke. Im converting a 27cc and will be running a 17" or so, but this guy runs the 32cc with a 20" in a 1/4 bipe . Look at his other videos,he's converted a 64cc as well as an 80. They are quality engines and last forever.
Maybe the 32 will do it for ya?