I will reiterate, that a shield is not used with an empty weapon hand. If you’re going to use a melee skill to use it, it needs to be one that is actually trained with in using the shield. melee (unarmed) should not count.
I think we are drifting into far more detail than Traveller rules support. If you drop your sword or are disarmed accident then by your logic you would suddenly become less capable of defending with the shield. There are historic cases where a shield was used with a non-melee weapon (particularly thrown weapons and slings). The futuristic shield and pistol is also valid.
Obvious the benefit of being able to hide behind it or use it as partial cover vs ranged attacks (the protection and DM-2) are independent of any weapon in the the other hand, so we can dispense with discussing that.
The question therefore is whether the Parry requires a weapon in the other hand. We cannot simply say it can't be used for Melee(Unarmed) as the game has a number of weapons that are used with Melee(Unarmed). It is entirely possible to bat away a rapier thrust with a bare hand and that is I contend a "parry" within the rules as it doesn't provide the level of granularity to cover all historical fencing moves. You can also snatch even an edged weapon away with a bare hand (as long as you get a tight grip so it doesn't slide and cut your hand). This is covered in the Grappling rules - Melee(Unarmed) again. The rules do not explicitly state you require a weapon for you to parry (and many martial arts also train parrying the weapon arm rather than the weapon itself).
I believe that the shield can either be used to supplement a parry using the other hand (by passively cutting down the amount of the body exposed) or it can be used dynamically to defend (blocking a blow itself). Both methods are used historically with the amount of active vs passive being generally inversely proportional to the shield mass. Traveller does not allow the granularity to detail this so it is entirely reasonable to gloss over it (given we are talking a 6 second combat round with movement, minor actions and reactions all compressed into it in a non-structured way).
You can use whatever Melee skill is appropriate to the weapon you are using (including Bludgeon as you could use the shield itself). It doesn't matter what you attacked with this turn as you don't even need to attack to be able to parry (but you need to be at least holding the weapon to be able to parry with it). Even if you are untrained in Melee and have no skill at all several shields grant it to you (as high as Melee-1) so clearly training with a weapon isn't necessary to be able to parry with a shield. Apparently picking it up is sufficient (which make sense if you just hold it against you to cut down on attack vectors).
Since the combat arm can be used to parry as if a shield then you could use a shield in the other hand and use it to grant a DM to the parry from the arm. Simply punching would use the unarmed skill so that is the appropriate skill for a parry as well. Since you can build a weapon into the arm you have multiple attack and defence options when used with an expandable shield (we'll assume it is deployed as a large shield).
1) Combat arm with spiked or brass knuckles to attack. Parry using arm with Melee(Unarmed) with DM+2 for shield.
2) Combat arm with built in knife to attack. Parry using knife with Melee(Blade) with DM+2 for shield.
3) Combat arm with a club held with the combat arm. Parry using club with Melee(Bludgeon) with DM+2 for shield.
If you are using the Companion (and possibly other supplements) you also have other Melee specialisms available.
Regardless of what you are holding you can parry using Melee(Unarmed) to parry with the arm in which case the shield provides the DM+2.
You always have the option to use Melee(Bludgeon) to parry with the shield (if you have a combat arm it will providing the DM+2).
Either of these could be substituted if the skill level was higher than the specific weapon you were armed with.
