There's something of an (unofficial) understanding that shock weapons are electric attacks that don't play by the same rules as kinetic attacks like unarmed strikes.
A shock attack is a touch-only attack where simple contact is the key element - it's more of a binary "yes/no" consideration - not the force of the contact like in a kinetic attack. The book's examples of "the shock kick" and "street head butts" make it reasonably clear that, per the Rules as Written, these types of attacks would only deal the shock damage, not shock + unarmed.
So, long story short, up until now almost everyone rules that the two don't stack. But, if you're like many people (such as myself) who are house ruling melee damage to incorporate Strength, then it's possible that shock limbs might need to be similarly house ruled to ensure that they don't fall too far out of balance.
Grappling, with prolonged contact, is another can of worms, but I don't know enough about how electricity grounds itself through living bodies to know if using a shock limb during a grappling attack will backfire on you.