What is the best Out Of Group class to pack around?

It is old school. I do get his intention, that he does want to concentrate on one character and this might even work with a shaman. However, he would miss the opportunity of two additional characters including a second merc which most likely will be a healer or DPS. With the shaman he would have to use the tank merc for most targets.

The idea to pim.p his main or a multiplayer group with an OOG char is not really logical, because that already is boxing, especially if he will drag that toon around with /autofollow. And no other class has more buff options than the shamy. Duo boxing is not that hard, and can only be puzzling for the first few days. I would just solo or molo with the shaman if I won't like boxing. A good compromise is hard to find and might be limited to a PoK buff mule.

I've dragged an OOG box around for different reasons quite a few times. It's miserable

The number 1 use for an OOG box is a cleric or some other class that can rez. Necros work really well if it is an area with no AEing mobs. Then you can just FD the necro or log the cleric out and then log back in or stand up and rez if something goes wrong. The necro also has the advantage of some splitting ability and could do pet / dots out of group to help kill faster.

Bard is good for being out of the group,
it has AE regen song
it has forage
it has track
it can pull enemies
it can navigate around easily
it can CC
it can also dps

its the only class where you can use many of its spells into a loop too, so less maintenance.

I have no opinion on which is the best class for an OOG box. By far the most common class choice is the streamer.

If it's just going to be a buffbox probably an enchanter. You'll want a shaman actually in the group for a lot of their better utility, same for a bard. Druid is more useful earlier on for ports, and for most of the TLP lifecycle for "most" players (as they won't play past GoD) but falls off a lot in usefulness unless you plan to constantly move around during your play sessions.

The only time I do is when I am camp firing in a buffer to top us off. I prefer not to otherwise.