Looks like you're in luck! The rom which would need hacking is socketed (SK1-1 at position 6B). The 6Kb of shared work/sprite ram is at the top right of the board (positions 8R, 8P and 8N) and looks to be socketed too. I can't find a schematic for Sky Kid but I'd imagine the hardware layout is identical to Pac-Land so I'd take a very strong guess that the middle one of those 3 is the one that would need replacing with a 2Kb NVRAM module, just like Pac-Land.
According to the Mame Sky Kid driver there are two different versions of Sky Kid which use the CUS63 chip (sub-cpu at position 3B marked 63A1). These are known as skykid and skykido in Mame. I'd need to know the 32-bit CRC value of the rom at position 6B before I started to apply the hacks so that I would be sure I was targeting the correct board that you have. Do you have an eprom reader so you can read the contents of that rom? Other than that it would be trivial to add to high score save to this board
According to the Mame Sky Kid driver there are two different versions of Sky Kid which use the CUS63 chip (sub-cpu at position 3B marked 63A1). These are known as skykid and skykido in Mame. I'd need to know the 32-bit CRC value of the rom at position 6B before I started to apply the hacks so that I would be sure I was targeting the correct board that you have. Do you have an eprom reader so you can read the contents of that rom? Other than that it would be trivial to add to high score save to this board