A question about unique interactions

So, I recently found a Vial of Volatile Ice and am getting a good amount of use out of the cold Acid Flasks, but I’m curious: do catalysts cancel out the “While Unarmed” aspect of Falcon Fists?

Definitely want to experiment with those when I find some, but would like to know if I’ll have to give up the Vial to get them to work for me.

Only the Main Hand slot needs to be empty to be unarmed