well actually there IS a MiG-27K but it neither is nor was intended to operated from a CV
;)
there was a Version of the MiG-23ML pojected for the use on carriers, which was designated MiG-23A but never went into testing afaik ;)
The Russian Naval Airforce uses: MIG-29K (2 in service) Su-33/Su-27K (24 build, one or two have crashed) Su-25UTG (naval Trainer attack version was proposed)
the Su-25 would be my choice for a carrier based attack aircraft ;)
otherwise you could choose the MiG-23A (there is a CV-Based Flogger in the D/L section calld "MiG-23MK") and the YAK-141 Freestyle (which is quite cool btw :-D)
you only have to manage two things:
you have to get:
the right time to break away
and the right time to flare, also your ECM should be turned on only when you are actually attacked, because it reveals your position ;)
if you get these two right, it's quite easy to get away alive ;)