Sorry I didn't get to these earlier:
Same goes with every kind of ‘Perception’.
If one knows how to hide in shadows, then one is better able to recognize someone else doing it. Add the Stealth skill proficiency to detect someone who is hiding.
If one has proficiency with Alchemist tools, then one is more likely to recognize a particular chemical by its smell.
Part of the idea, here, is to remove the disconnect between 'player knowledge' and 'character knowledge,' so, all the Knowledge-oriented skills go with INT: away.
Proficiency in Alchemists tools might be rolled, probably with DEX, to perform a delicate preparation without dropping something at the wrong moment and blowing it all up. Proficiency with stealth would be rolled to move very quietly (presumably with DEX), or hold very still while hiding (possible CON would make the most sense, there). Finding a place to hide, avoiding rustly leaves or squeaky floors, would be up to the player.
That's certainly a viable option. However, it turns Stealth into a godly skill. The ability to both hide and spot ambushes is incredibly potent.
That'd be problematic, but it's not what I was thinking. Stealth would just be about avoiding making noise (or whatever). Perception is handled strictly by DM-player interaction. If the player sneaks up on something, the DM uses his degree of success or failure, and his judgement of the victim's alertness to determine if he gets surprise or sneaks past. If someone's sneaking up on the PC, the DM can roll stealth behind the screen, and describe what the PC perceives based on the degree of success/failure. From "you hear a loud crack and whispered swearing coming from behind you," through "on you watch you hear crickets and the occasional rustle in the bushes," (which the player could investigate or not)to "the night is still, quiet, & uneventful on your watch, until you feel a sharp pain in your back..."
DM devices like carefully worded descriptions that give the player the information that they're being snuck up on or about to trigger a trap or whatever, /but only if they notice the specific phrasing buried in among a lot of trivial/distracting description/, could be used liberally.