Building a custom holster would be the best option.
I don't even think the tactical vest can hold a warlock axe. I meant it can hold a small blaster. I'm sorry if that was unclear.
Best of luck on building a holster for the axe.
Nerf does not make holsters for weapons as far as I know. I do believe the tactical vest can hold one or two smaller blasters.
I believe you should be able to make one without too much trouble. (I know, not the answer you were looking for.)