Agreed it's highly likely to be a transcription error most probably caused by the unusual name of Clyde.
I can imagine widow Helen Clyde Cogger taking Edgar along to be baptised alone and the entry being made accordingly (although I'm not sure whether the father should still have been named even if deceased, I think a father has to be present to be named as such?), as the parents names are entered in the same box (eg John AND Mary) I think the transcriber has read Clyde as a male hence father's name, not noticing the entry did NOT say Helen AND Clyde.
I've searched A's births for the period 1860 to 1870 for all births under Edgar (18) or Cogger (13) or Nash (23) in Cranbrook.
Nothing resembling which could be typo error's.
Helen & James wed in 1866 and assuming not a shotgun wedding ?, Edgar would have been born in 1866 to 1868 (allowing for a 9 month period from the year of James' death). The nearest result I could find was a birth for James Cogger in Cranbrook 1968.
This is the point at which the desperate "what if's" start......what if Helen changed her mind about the name between the formal registering of the birth and the Christening

Can I confirm you state Edgar's birth date 1869 but you assume you mean Christening?
Steve