From the Bestiary, Cairn Wight (CR 4):
Some societies deliberately create these specialized wights to serve as guardians for barrows or other burial sites. A cairn wight is an advanced wight that fights with a weapon, typically a sword, that channels its energy drain attack and affects creatures damaged by the weapon as if they had been struck by the wight’s slam attack.
The variant monster description says it typically fights with a sword, but does not specify that it must use a melee weapon to channel its energy drain special attack. I am not aware of anything published by Paizo that prohibits a Cairn Wight from channeling its energy drain with a ranged weapons, so can it do so?