Are you carrying some other backpack? You really ought to have a few supplies along on any non-trivial outing, and a framed child carrier is a decent place to carry those if you also expect to carry a kid at some point.
If the rest of the party is capable of carrying all the supplies I would consider an inward facing soft carrier for the back. I've used an ergo brand one pretty comfortably to about 50lbs which is about as heavy as I care to do with camping packs. If it is hot or hard work sweat is often significant and it has nowhere to go so can get my back and the kid's chest fairly wet, but if you are just planning on shorter stretches that shouldn't be as big an issue.
Also most kids seeing a carrier will expect to be carried at some point, which ought to be planned for. The soft carrier I use is about as bulky as I feel comfortable stuffing into a daypack. Wraps are a lighter alternative, but are a little less convenient to get into and out of. That might not be an issue if you aren't really expecting to use it, but I would practice once or twice because there is a learning curve. One kid was also bothered by being tied in even though he didn't have access to the fasteners of other packs anyway.
How much more work is this than they normally do? If they do even half the distance on around town outings I wouldn't bother with a carrier, and instead consider motivational techniques and extra breaks.
Depending on how strong you are carrying piggy-back or on a hip without any equipment can also work. I don't like carrying kids more than around 20lb on my shoulders for more than a few hundred yards because it bothers my neck and can bother their legs, but on a hip or piggy-back I can give a child a reasonable rest. And if you can pass the kid between a few people willing to carry them this can even work over long distances.