There are no silly questions here, so we’re all good. 
As far as the ‘best’ loadout goes, and due to a heavy reliance on Zane’s kill skill buffs, the suggested build isn’t particularly gear dependant. While this means that there’s not really a ‘best’ loadout as such, the good news is that plenty of options can give you great results.
As mentioned briefly in the guide, Playing Dirty lends itself to high damage per shot weapons, so choices like Jakobs shotguns/pistols/snipers are often a pretty good starting place.
I can understand you wanting some specific recommendations though, so here’s a couple of quick ones:
I’ve really been enjoying The Duc as my primary weapon lately. I’ve found it great for mobbing and bosses alike, and don’t have any problems critting/proccing Brain Freeze with it at all. Interestingly, The Duc I’m using is notably under levelled (L44, running some L50 Mayhem 2 with it right now), but it’s keeping up with the rest of my loadout for the most part. Personal tastes will vary of course, but I’m having great fun mobbing with it so far. I’m all for choosing the weapons you find the most fun.
One Pump Chump is another found in my current loadout, and a solid go-to shotgun choice all 'round. You won’t proc Brain Freeze as often with this as you might with higher ROF options of course, but I still get a great deal of utility out of the skill, and consider it worthwhile.
I’ve even been dabbling with the Monocle sniper a bit lately too, though need to spend a some more time with that one I think. The Flakker, and The Cutsman can all do some work for you in different situations, amongst others.
Based on my current loadout, I’m also using the re-router at the moment. If you’re wanting to add some higher ROF options though, a different shield would certainly be the way to go.
In short, you have a lot of loadout flexibility with this build, but as you’ve rightly pointed out with the Re-Router example, you do need to tailor your choices to the skills selected.
Does any of that help at all?