There are two fundamental questions here:

• Does damage prevention apply to a single head or to the team (i.e. can creatures attack "the head that doesn't have prevention" and still deal damage)?
• Does landwalking apply to a single head or to the team (i.e. does a creature with swampwalk have to attack the player who controls swamps)?

I think the answers are "yes" and "no", respectively; That is, damage prevention applies only to a single head, while landwalking applies to the "defending player" (which is the defending team) as a whole. As such, you can bypass the prevention by attacking "the other head", and landwalking will still work for you even if that head doesn't control any swamps. I'll check the comprules when I get the time.

EDIT: Comprules!

806.7f As the combat damage step begins, the active team announces how each attacking creature will assign its combat damage. If an attacking creature would assign combat damage to the defending team, the active team chooses only one of the defending players for that creature to assign its combat damage to. Then the defending team announces how each blocking creature will assign its combat damage. See rule 510.1.

and:

806.9. Damage, loss of life, and gaining life happen to each player individually. The result is applied to the team's shared life total.

Since Noble Vestige prevents the next 1 damage to a "target player", and two-headed giant never says prevention effects work on the team as a whole (I looked, there's no mention of 2HG with prevention anywhere), you can definitely have your creatures deal the damage to the player without a regeneration shield (and the result would be applied to the team's shared life total). So the answer to the first question is "yes".

Let's continue:

806.7b Any one-shot effect that refers to the "defending player" refers to one specific defending player, not to both of the defending players. The controller of the effect chooses which one the spell or ability refers to at the time the effect is applied. The same is true for any one-shot effect that refers to the "attacking player."

Any characteristic-defining ability that refers to the "defending player" refers to one specific defending player, not to both of the defending players. The controller of the object with the characteristic-defining ability chooses which one the ability refers to at the time the nonactive players become defending players.

All other cases in which the "defending player" is referred to actually refer to both defending players. If the reference involves a positive comparison (such as asking whether the defending player controls an Island) or a relative comparison (such as asking whether you control more creatures than the defending player), it gets only one answer. This answer is "yes" if either defending player in the comparison would return a "yes" answer if compared individually. If the reference involves a negative comparison (such as asking whether the defending player controls no black permanents), it also gets only one answer. This answer is "yes" if performing the analogous positive comparison would return a "no" answer. The same is true for all other cases that refer to the "attacking player."

And this means that swampwalk, which officially means "this creature is unblockable if defending player controls any swamps", applies to the team as a whole; the answer to the second question, then, is "no".