If a special damage type (fire, sonic, shock, etc) is added to a weapon that deals nonlethal damage (whip or sap), is the special damage also nonlethal?

Or would the weapon damage be nonlethal, and the special damage be lethal?
and
In the case of the whip, because it deals a special damage would it then be able to hurt a creature with an armour bonus?

The whip damage would still be non-lethal but added damage would be lethal. Imagine getting hit with flaming whip. The whip would just hurt but the fire would be potentially deadly. I would not allow it in my campaign as a DM as it would be a nightmare keeping track of multiple damage types.

I was thinking about having a shocking whip. And the Dungeon master hasn't vetoed the idea, but wanted me to find out how that worked.

So would you say then, that to use a whip against an armoured target, it would be a ranged touch attack then, because I am just trying to touch the whip to the target to deal the shock damage?

In that case yes a "shocking whip" would deliver lethal type electric shock. I would likely play it that a successful attack with the whip would allow either of two options:

1. Roll a second attack roll to see if the shock damage occurs

2. Assume auto shock but have the target roll vs spell to determine damage taken.

The weapon is just the delivery system. I'd see this weapon the same as a rod or staff that would deliver a shock attack. So the rules for rods and staffs would apply. Then it would depend on the weapon rules set you are playing.

Yes a ranged touch attack as you are trying to touch with the whip to allow the shock damage.

Thank you all for your replies. It was very helpful.

And I hope you all have a truly Merry Christmas!.

Depending on your ruleset, a whip already has been defined as a melee weapon, with 15ft reach. It provokes attacks of opportunity like a ranged weapon. You literally are just adding your energy damage to a standard melee attack. No ranged touch attack, that would be cool and all, but you actually DON'T deal damage to a creature with armor on. The energy would, but the whip does not. It's a niche weapon. For instance, you can use weapon finesse to apply your dexterity to the attack roll instead of your strength.

I'd have to do more research to find out whether or not the magical enhancement would override the damage penalty to armour or not. But there you have it, my understanding of the rules.