What I'd prefer - and this'll put me in the minority yet again, but so what - is that abilities intrinsic to the character that don't tie to one of the six core stats use their own subsystems.Wisdom should be about mental strength/willpower than sensory perception anyway. Roll all that stuff into a separate searching roll.
Listening is one such. Sharpness of vision is another. None of the core stats affect how well one can hear, or see; and those two senses are by far the biggest inputs into perception. Species might have an effect e.g. Elves are known for having sharper-than-Human eyes while Hobbits are very good as hearing sounds, and that can be represented by a small bonus when rolling for such.
Thus, perception (and by extension, observation) should use a separate and somewhat fluid subsystem - one doesn't have a "perception score" as such but instead has a few bonuses (or penalties) to put on a roll the DC of which will be different every time as determined by the DM based on the in-game situation.