I assume you mean dual wielding 1-handed ranged weapons, or do you mean pistol+shield/offhand?
Cold Fire Strike Purifier may be possible with Mythical Chains of Nightfire and Galeslice’s Mark as a starting point, though I haven’t really thought this through and I’d guess you’d probably get better results with The Desolator or Ugdenbog Arcaneweaver than by dual wielding pistols.
You may also be interested in looking at an Infiltrator build @tqFan put together a while back for some ideas, though it does have a number of fantasy green items:
[Feedback] The Great Ranged Balance Discussion
(grimtools for that build here 
)
https://www.grimtools.com/calc/RVvw3jXZ
One takeaway here is that since it can be hard to convert both fire and lightning, one approach to make things easier is to start with no real fire or lightning in the first place and instead grab more natural pierce and vitality to cold conversions and corresponding devotions.
Trying to convert all/most of Attak Seru to cold, which is what I assume you’re shooting for when you say
is super ambitious and seems like it forces a lot of gear choices that can leave you lacking in stats and/or key skill points.
I think you probably have to start by ruling out all pistols except the cold or elemental ones with attack speed.