If Cherche's Axe can be refined, wouldn't it be better to refine it to +Atk for more power?

Depends on you, really. Panic Ploy is one of those skills that's nice to have, but isn't necessary, especially since it relies on the foe having visible buffs.

But you're only getting, what, 2 attack out of the attack refine? At that point it's not really worth it in my opinion.

From playtesting so far, I’ve been considering refining for the extra attack. 2 points of damage doesn’t seem like much, but it will secure a pretty ridiculous kill....+10 Zelgius with Steady Breath will die to +10 Cherche if you go all in (SS, AS, Hone Flier buff, x2 goads nearby) Not a feat that’s necessary but still pretty friggin amazing she’s capable of this

If you're using her in tier 20+ arena, everyone has dual rallies, tactics, and waves. With Panic Ploy you may be debuffing for a lot more than 2 Def, which makes the potential far greater than +2 Atk. Not to mention it can help her teammates.

Of course, Panic Ploy application is less consistent due to positioning and HP requirements. However, as a flier Cherche is more flexible in her positioning than other movement types and as long as she's not -HP she can inflict Panic on many armors and some dragons, particularly since most people like to run them with -HP.

With summoner support, she can inflict Panic on basically everyone but the highest HP armors.

If you have either the C-Slot or Seal slot open, I think a +Atk-refine with Panic Ploy in one of the other slots is the best course of action. (Recall that the Special refine only gives +3 HP, while the other refines provide +5 HP along with a stat buff of your choice, meaning that you get more stats to mess around with and even more HP to Ploy with.)

But if you can't afford to give up any of those slots, then Panic Ploy refine is still pretty good should your team need that utility more.