Have a character who is staying away from Lightsaber, but wants to be a melee and brawl character. Is there any specialization and talent(s) in any of the books that allows for Agility to be used instead of Brawn? They see themselves as scrawny, but martial arts type of character.

Not specifically what you're asking for. Closest thing is the Tail of Selonian characters (from Suns of Fortune). Essentially, when a Selonian does a Brawl attack with its tail, and only when it's using its tail, it gets to use Agility and gets a +1 to damage, but damage is still based on Brawn.

If you were so inclined, you could probably homebrew a couple specialization trees that include a talent that allows Agility to be used instead of Brawn for Melee or Brawl attacks, but still using Brawn for damage. But, I wouldn't make it so that a single tree had a talent/s that allowed Agility instead of both Melee and Brawl since obviously learning the equivalent of an unarmed martial art form and learning to wield a variety of weapons (since Melee does open up the use of a large variety of different weapons) are completely different and would deserve their own specializations.

If you'd rather stick to what's in the book, the Marauder specialization in EotE provides a number of Feral Strength talents to increase Brawl and Melee damage, which would be useful for upping Brawl damage despite having low Brawn. And the Ancient Sword allows the use of Lightsaber skill (and subsequently the different Technique talents if the player has a force rating), and so effectively the player can be using a non-Lightsaber melee weapon with Agility that way.

I would make only for unarmed using agility for attacks but not for damage

I'd actually say the better representation of that would be to buy a lot of ranks in brawl rather than allowing for agility to be used.

Say you have your weak martial artist with a brawn of 2, but he's been training like crazy to overcome his naturally small frame. Assuming you start with a spec that gives you 2 free ranks in brawl at character creation, you're starting with 2 proficiency dice on your brawl checks. After the first session, you spend your xp to get another rank in brawl, and repeat until you're happy with it. Maybe you go all-out and bring brawl all the way up to rank 5 asap for 60 xp over your first three sessions, now your martial arts master is rolling 2 proficiency and 3 ability dice against the measly 2 difficulty dice of the standard difficulty. He's not naturally strong, but his intense training has pushed him to ridiculous levels of prowess.