
Mysterious Stranger |

Looking over the undead entries in the bestiaries they all seem to list the drains under the attack section. Shadow for examples shows Melee incorporeal touch +4 (1d6 Strength damage). That seems to indicate that the undead has to touch the character, not just be touched by something for the drain to happen. Looking at the description of the shadow this is clearly stated. Strength Damage (Su) A shadow's touch deals 1d6 points of Strength damage to a living creature. Every undead I looked showed the same thing. That seems to be a pretty clear indication that the undead must actually touch the character to cause the effect.
So, unless the undead creatures stat block specifically states touching it cause the drain, it probably does not.

Dragonchess Player |

Generally speaking, it's a good idea for a monk to carry a manufactured weapon as a backup to deal with DR/[substance] and/or when facing enemies (such as oozes) that cause damage when using natural weapons/unarmed strikes to attack them. Even if you don't use it all the time.