Answer:
The short and naive answer is about 160. But this question is really one of those questions which have no clear-cut answer, because...
[1] Many of the shows were co-written with other people (notably Larry Stephens). In some cases entire shows were written on his behalf.
[2] Some of the stories were redrafted and rerecorded over the years.
[3] The early shows were not Goon Shows as we would recognise them. They were more like variety shows with a mix of music and comic sketches that may or may not have familiar Goon characters in them.