There is a class (or lineage) for all four other abilities
These are ways I know of that allow you to use ability scores other than Dexterity or Strength to enhance your melee attacks:
Damphir Lineage (Van Richten's Guide to Ravenloft): Vampiric Bite feature allows you to add your Constitution modifier instead of Strength with the bite.
Druid 1: The shillelagh cantrip allows you to use your spellcasting ability, Wisdom as a druid, instead of Strength. (Likewise, feats that let you pick up the cantrip, such as Magic Initiate). Duration one minute on club or staff.
Hexblade Warlock 1 (Xanathar's Guide to Everything): Hex Warrior feature that allows you to attack with your Charisma modifier instead of Dexterity or Strength. Works only with your pact weapon.
Way of the Astral Self Monk 3 (Tasha's Cauldron of Everything): Arms of the Astral Self feature allows you to attack using Wisdom modifier instead of Strength or Dexterity with your astral arms.
Artificer Battle Smith 3 (Tasha's Cauldron of Everything): Battle Ready feature allows you to use your Intelligence modifier instead of Strength or Dexterity, when attacking with a magic weapon.
Artificer Armorer 3 (Tasha's Cauldron of Everything):
"Each [Arcane Armor] model includes a special weapon. When you attack with that weapon, you can add your Intelligence modifier, instead of Strength or Dexterity, to the attack and damage rolls."
Bladesinger Wizard 14 (Tasha's Cauldron of Everything): Song of Victory feature allows you to add your Intelligence modifier to the attack.
How to best realize your character concept?
Your stated goal (from the comments) is that you would like to play
a common farmer who is, in fact, a heavy hitter. (...), he might look average and even remain undetected by a Battle Master's "Know Your Enemy."
You should realize that no player character is "a common farmer", all of them are highly exceptional and have class levels due to being so. A common farmer would be a commoner, with ability scores of 10 across the board, so which ability you use would not really matter.
If your secondary goal is that someone cannot assess you correctly with Know Your Enemy, then none of the options will fully protect you, because Know Your Enemy will always work to reveal how powerful you approximately are, no matter which classes you picked, with this choice:
- Total class levels (if any)
But worrying about that feature is entirely unnecessary: Any character with class levels, if PC or NPC, is already rare, those of 7th level or higher are rarer still, and those that happen to be (complicated to run) Battle Masters, are yet again more rare. You'd be unlucky to have that happen to you a single time in your average campaign, and even if it did, it would not be a big thing.
To realize your concept of appearing as a harmless, normal peasant while in fact being a powerful melee combatant, classes that do not need a lot of unusual equipment that will give them away will be a much more effective and simpler choice than worrying about the ability score that gets added to melee attacks.
The options that allow you to do it at level 1, druid or warlock, seem to be the best here, along with the monk. They do not need to wear heavy armor or carry martial weapons to be functional.
If you want to use a hoe, as you added as info in your comments, then either the hexlade warlock or the battlesmith artificer would be good options; both warlock can use any weapon (you also need to be 3rd level for a two-handed weapon). The artificer needs a magic hoe for this, but that should not be a problem, as he can infuse the hoe to become a magic weapon. A hoe is not a standard weaopn on the weapon table. Check with your DM which weapon they would like to reskin.