There a plenty of skill-based systems (like BRP) with extensive lists of skills, but a few common skills could be a good way to add variety to your Fighting Fantasy character without adding much more to the rules.
Adventuring SkillsStealth: The first thing you want to try is sneaking past that guard.
Tricks & Traps: Finding the location of that hidden latch, tampering with a trap, opening a stubborn lock, detaching a tempting purse.
Persuasion: A bluff, a clever lie, or a call to a higher purpose, even striking a good bargain, all require persuasiveness.
Bind Wounds: Any form of rough healing, or first aid after battle.
Strength: Not simply training and endurance, but knowing the point of leverage, or where to exert pressure when you break open a chest or smash down a door.
Hunting & Tracking: There's always game to pursue and tracks to follow in the wild.
Wayfaring: It's useful to know the hidden paths, the landmarks, the places of safety and concealment.
Learning: Reading is one thing, but this character knows how to decipher an ancient script, the name of that demon, that crucial fragment of old lore. Speak, friend, and enter!
How to use the skills
Skills are not just training, they're habits, strategies, approaches. In a simple FF game, offer characters three skills when they're created. Then, if the conditions are right, the skill confers a +1 or +2 bonus to action. This can be added to SKILL (or WITS, if you use that option), or even a probability roll.