I'm working with a setting that uses a lot of distinct melee weapons. Obviously, I'm using the Melee Light and Heavy skills. In the setting, there are distinction between "characters who are wielding a sword" and "characters who are wielding a spear" and so on and so forth. While both of these could fall under one skill, I'm trying to create options that distinguish these further.

One, do I split melee up a bit more, perhaps having a skill for a few more weapon types?

Or two, do I just introduce talents that focus on a single weapon type? "When wielding a spear..."; "When wielding a blunt weapon..." etc.

I think that it would be best to use talents to make the different fighting styles distinct.

Adding a new skill will require more Xp for a character to get into it. However, if you start putting in Skills for various Weapon Categories, you'll have a long list and some complications (arguements of what weapon is what category or bridging two categories, etc.). I find having Melee Light being all One Handed Weapons, and Melee Heavy being Two Handed Weapons is enough distinction while not over burdening players.

As for Talents, Star Wars has made the exact same exclusive talents like you mention (Lightsaber, Melee, or Brawl Weapon, etc.), so I find that to be a good way to go.