Decarboxylation of cyclohex-1-ene-1,2-dicarboxylic acid by electrolysis method
Turns out a similar reaction has been performed,   the reaction proceeds via the following mechanism


  
  SOURCE  


The cyclohexyne dimerizes to 1,2,3,4,5,6,7,8-octahydrobiphenylene. Then further rearranges. So I would say that electrolysis is feasible with rearrangement as depicted in the picture .
 The second compound(1,2,3,4,5,6,7,8-octahydrobiphenylene) which you've drawn is more stable since very unstable compounds (cyclohexyne) do not form even more unstable compounds. The second compound will not be the final product/major product owing to its high instability due to anti aromaticity.



PS
 I haven't delved into the details regarding the instability of cyclohexyne and 1,2,3,4,5,6,7,8-octahydrobiphenylene since they have been well covered in Gaurang's answer