At first level the possessed shaman gets the Shared Skill ability, and later a similar ability to add another skill to it.
If I choose two dex- or strength-based skills for shared skill, they become wisdom based. That should mean, that they are not penalized by armor check penalty anymore because only dex and strength based skills have ACP. Right?
As long as I do not find any evidence in the contrary I'll assume it works that way. The discussion about the circlet of persuasion seems to indicate that changing a skill's stat bonus from one stat to another makes it based on the new stat.
I'm going to agree with you, doesn't seem to break anything.