TL;DR

I suggest to take Animal Ken, Athletics, Contacts, Crafts, Doxa, Empathy, Episteme, Fight, Manipulate, Notice, Perform, Physique, Resources, Sail, Shoot, Stealth and Will, taking inspiration from existing games set in mythological Greece.

Steal from similar games

There are a few games out there that have a similar setting, so let's have a look what they list as skills for characters. Assuming the authors there did their research and spent some good time thinking about which skills to include, this should give good pointers towards creating a good skill list for this Fate game.

Disclaimer: I have played neither Fate Core nor any of these games, so please feel free to consider this a bad answer.

Arete

Arete is a game by Nicholas DiPetrillo. It is set in Greek mythology, trying to recreate Hero stories of Greek mythology. Its skill list contains the following 21 skills, corresponding roughly to the Fate Core skills listed:

• Archery (Shoot)
• Allure (Rapport)
• Wealth (Resources)
• Armed Combat (Fight)
• Authority (also Rapport?)
• Defense (Athletics)
• Craft (Crafts)
• Might (Physique)
• Deception (Deceive)
• Sailing (Drive)
• Entertain (Rapport, again)
• Sneaking (Stealth)
• Nature (Lore)
• Swiftness (also Athletics)
• Oratory (a fourth implementation of Rapport)
• Toughness (a second aspect of Physique)
• Perception (Notice)
• Wrestling (either Fight or Athletics)
• Religion (also Lore)
• Resolve (Will)
• Underworld Magic (third Lore ability)

Absent are the Fate Core skills Burglary, Contacts, Empathy, Investigate and Provoke. Instead, Rapport, Lore and the skills used for fighting are split into multiple implementations.

Spartan

Spartan is a two page rpg designed by McEachern for a two-page tabletop RPG competition, in which players take on the role mythical ancient Greece. It lists 12 skills:

• Crafts: Building, repairing, sabotaging mechanical objects. (Crafts)
• Curses: Inflicting misfortune, particularly having to do with vermin (snakes, rats, insects) or the weather. (Lore?)
• Diplomacy: Bartering, soliciting aid, building rapport. (Resources, Rapport)
• Hunting: Ranged attacks, tracking, animal handling. (Shoot, Notice)
• Illusions: Masking real things with false images. (Deceive, Lore if magic?)
• Influence: Buying things, knowing people. (Resources, Circles)
• Lore: Knowledge of history, languages, geography, etc. (Lore)
• Performance: Playing music, dancing, acting, lying. (Rapport, Deceive)
• Physique: Running, wrestling, kicking down doors. (Physique and Athletics)
• Prophecy: Talking to animals or the dead, who may sometimes offer cryptic hints about the future. (Lore)
• Subterfuge: Stealth, attacking unsuspecting targets. (Stealth, Fight, maybe Burglary)
• Warfare: Melee attacks and tactical maneuvers. (Fight, mostly)

Absent from this list are again Burglary, Empathy, Investigate and Provoke. This game has multiple ways to express Rapport and Lore, as well.

Agon

Aγων is a competitive role playing game, again about mythical Heroes of ancient Greece. Its skill list sports the following 16 abilities:

• Insight: awareness, reason, and wisdom. (Lore, Notice)
• Grace: agility and poise (Athletics)
• Might: physical power, both strength and vigor (Physique)
• Spirit: power of the will (Will)
• Heal: used to remove wounds (Lore or Physique)
• Lore: information through careful study, observation, or obscure knowledge (Lore, Investigate)
• Music: playing of instruments as well as recitation of poems and tales. Music may also be used to soothe beasts. (Lore, Rapport)
• Orate: speak to others and have an effect on them, positive or negative (Rapport, Provoke)
• Athletics: running, jumping, swimming, and climbing (Athletics)
• Cunning: stealth, subterfuge, deceit, camouflage, or trickery—and also for resisting those things (Stealth, Notice, Deceive, Empathy, maybe Burglary)
• Hunt: track, set and detect snares, tame beasts, and other woodscraft (a variety of skills)
• Wrestle: grapple, throw, and pin an opponent (Athletics, Fight)
• Aim (Shoot)
• Shield (Fight)
• Spear (Fight)
• Sword (Fight)

Agon really splits down Fight, and still has multiple versions of Lore and Rapport.

Skill list for a Fate Core game

Given the observations of those games set in a more mythical Greece, I suggest the following changes.

• Drop Burglary, its trappings go to Stealth.
• Drop Investigate, and use whatever Lore becomes, plus Notice and maybe Circles.
• Due to the mystical element, Lore should be at least split into something like Doxa/Faith/Religion/Magic and Episteme/Knowledge. Doxa might be used for magic attacks as well as for the basic Lore trappings, given permission through Aspects or Stunts.
• The social skills need some adjusting. The split seems to generally run in the methods, and not in the results, so Rapport and Provoke are mingled into something like Perform (in front of an audience) and Manipulate (on a more symmetric level). Manipulate might eat up Deceive, as well. This reduces the number of social skills, which seems apt.
• The Greeks have three radically different ways of getting around: carts/chariots/…, horses and ships. This suggests renaming Driving into Sail, and if you don't want all the animal skills handled with Athletics and Notice, and Animal Ken skill might be appropriate. This is also possibly good to use instead of Provoke and Rapport to pacify Cerberus, get a Monster to come out of its lair etc.

This leaves the skill list as: Animal Ken, Athletics, Contacts, Crafts, Doxa, Empathy, Episteme, Fight, Manipulate, Notice, Perform, Physique, Resources, Sail, Shoot, Stealth and Will.