Non-weapon skill that has various effects on alchemy: make alchemical blasts less common (or zero at high skill), and increase the probability that mixing certain potions yields the right result.

Add “magical writing” as a nonweapon skill, which is trained at a fast rate by writing scrolls and spellbooks, and increases your odds of writing unknown scrolls and spellbooks successfully.

A levelable haggling skill that gets you better prices in shops.

Non-weapon stethoscope skill, which gives less information than it currently does at Unskilled (perhaps just HP), the same amount of information as currently at Basic, more information like pet tameness and apport at Skilled, and a full probe at Expert. Possibly it also takes a full turn to use until Basic or Skilled.

Swimming skill: how well you can swim on top of water and carry weight at the same time. At Unskilled you can carry very little, but it quickly increases beyond that.

Rangers can chat to certain animalistic monsters to calm them and make them peaceful (but not tame). Possibly generalize this into a skill that can be achieved by Cavemen, Monks and Tourists too.

Add herblore (possibly as a non-combat skill). This allows you to brew various potions using herbs and potions of water. Healers are quite good at it, and their quest contains many herbs. Requires actually implementing herbs, which cannot be planted or grown like in ADOM.