Hi Mark,
Welcome...
I presume we mean "attaching" to a wall and not repairing something...correct?
If so, "key ins" such as a peg are the very best method and usually the easiest to facilitate. Conduit on the outside of such a cobb wall is rather unsightly aesthetically and there are other methods perhaps to consider?
The other choice is "direct burial" into the wall, or creating a wainscott and placing the wiring and other mechanicals in it. I do like wainscott and it adds another textural element to the wall, and if design well can facilitate future changes/augmentations to such things as wiring and such.
Regards,
j
