ah, i was a bit confused since as of now i don't see very many skills that the character can use in combat.
but for overworld stuff, i think they should have an influence on fights but unless theres a high power imbalance not beat them entirely.
say you were to have an overworld skill that let you make a charge attack with your weapon in the overworld. if you manage to hit it you start the combat with an extra first attack. though if the enemy was very significantly weaker than you (like you would one shot them anyways) then it could be an instant kill.
shooting an enemy on the overworld could have a similar effect. if it doesn't one shot them then it would simply weaken them for when you fight them.
basically, stuff that gives an advantage in a proper battle, but won't win it altogether unless you would have already won easily anyways.