PoE 2 0.4 Fury of the King, but can I use cold dmg instead???

So I’ve been seeing some really awesome shaman bear builds using rampage and herald of ice for insane clearing. I’ve also been wanting to use the Fury of the King unique talisman just because the skill and design are pretty cool, but the problem is that all the phys damage is converted to fire w/ FotK, but what if I used the Blueflame Bracers unique? This unique converts all fire dmg to cold dmg which, if I’m not mistaken, should proc HoI for maximum carnage while looking awesome in the process. Now I’ve seen some conflicting opinions about whether the gloves actually convert “all” fire dmg to cold, but at face value, this seems like it would work. If anyone has an opinion or knows more about these types of conversions and if HoI would even be usable in this build, please let me know!

P.S. I also posted this thread in the builds forum, but I wasn’t sure if it would actually classify as a “build” so here it is again.