Something with no internal structure can't Swallow Whole. A zombie could conceivably Swallow Whole, but not a skeleton, barring magical aid (such as a force field of some sort cast on the ribs, but this is more trouble than it's worth). If a skeleton used Swallow Whole, then it would simply scoop something into its mouth and hold it there, assuming it didn't fall right out; it would be more like a prison than digestion. No bludgeoning damage from swallowing, no acid from digestion, and anybody with ANY sort of Strength, Dexterity, Wisdom, or Intelligence score could find a way out of the spaces between the ribs.
No sort of Skeletal cohort could swallow something whole, and a cohort is different from a minion or an NPC. Skeletons and zombies are mindless, meaning that they are the minions of whoever controls them. An NPC is an independent under the control of the DM, meaning that they could help or hurt you. A cohort is a character under YOUR control, but they have a free will; most undead do not. And mindless undead usually only obey those that create them, which isn't you, unless you have considerable necromantic powers (reanimating a Large or Huge creature, the only kinds capable of practical use of swallow whole, is either difficult or impossible). In addition, undead are usually evil, meaning that unless you're in an evil campaign, it's a bad idea.
Also, cohort usually implies something of at least some intelligence. I don't think an animal qualifies as a cohort, and a Bullette has an intelligence score of 2 - animal intelligence. You don't use Diplomacy and Leadership (or similar cohort-attracting methods) on something of animal intelligence - you use Handle Animal or Wild Empathy. The intelligence score must be 3 or higher to be a cohort; the Gray Render is monumentally stupid, but still cohort or NPC material with an intelligence score of 3 (barely sentient). A mindless creature thus doesn't qualify as a cohort at all - it is a minion.
If you don't care about cohort levels in respect to player levels (and I'll bet you don't), or you're in a high-powered campaign, please, consider a Remorhaz. The Remorhaz is wormish and capable of swallowing whole, along with burrowing. However, they cannot speak, so I don't know HOW you'd get one to agree to be a cohort, short of telekinesis. But if you're starting the game with a cohort (something I'D never allow, but it's not my game), then it is assumed that you made contact somehow, so don't worry about it.
