i can come up with several tho 
since it’s a mage hunter you could use a pierce dmg pistol; which would enable you to use inquisitors Ranged Expertise for more %pierce dmg boost on top
but, since the build (currently) struggles for cast speed my choice would probably be a green with with cast speed affix, like pierce dmg prefix dermapteran slicer “of Celerity”/fury, (will be biased towards attack speed but Celerity derma slicers still drop ok “frequent” enough)
or one of the MI pistols with a cast speed suffix and pierce/all dmg prefix, - this way you get pierce dmg and needed cast speed and also get ranged expertise passive boost on top
^“unlikely” affix due to vitality dmg bias, but Ugdenbog Howler has native cast speed, so a “Heart piercing Howler of Celerity/Fury” would be fantastic
Viper Haemorrhage you can shop in ToH, getting a pierce prefix and cast speed on it isn’t super hard if possibly tedious
madlee used a Heartpiercing of Celerity Ugdenbog repeater for his pierce casting aegis build (pistol gave native bonuses to shield that was used too, but essentially same +dmg and cast speed desire concept as here)
Officer, Tyrant, Heart Piercing and Sinister would be 4 useful/desired prefixes with %all dmg or pierce dmg, then you have “of Celerity” as magick suffix, or “of Fury” as rare suffix with cast speed - any combination of the those 6 affixes would massively outclass the current axe despite losing +3 AoC
i’d even venture a generic pierce pistol with +1 inquis would be better just from gaining ranged expertise %pierce dmg on top too aside form the geneal wide skill boost (death sentence etc)
Aethereach gives flat dmg to AAR, but also cast speed, so should be worth the loss in %pierce dmg overall, - but even if it wasn’t the case you still have Quickdraw gloves with %pierce dmg and more cast speed, or even %all dmg gloves with more cast speed, either of which would be better
*edit, there even is a blue pierce dmg pistol with cast speed it seems
Mythical Shadowspine Enforcer - Items - Grim Dawn Item Database