I have been summoned!
You are correct Delaque are hard to play well. They're often out gunned and will lose fire fights. You need to play carefully, otherwise they fold quickly. In general your Master of Shadows, Phantoms, and Nacht-Ghuls are going to be doing your heavy lifting.
Nothing is jumping out at me as "wrong" with you list. However, you do have 3 web weapons. I'd make sure your soon to be former friends are ok with that. That said using other weapon will certainly make your list "weaker". Outside of you're web weapons and Nacht-Ghul you don't have too much going on firepower wise.
I like Psy-Gheists, however they will be a "dead" model on the table until they get some experience (2-3 Willpower upgrades) and a Wyrm or two. What whisper did you give them?
Some things to think about:
- Is you group "power gaming"?
- Are you guys going for more of narrative campaign (the recommended way to play Necromunda)?
If the latter consider giving each model a unique "personality" rather than duplicated load outs.
Some changes to consider:
- Drop one of the web pistols shadows, and consider making a Ghost with a nice pistol like a Flechette, Plasma, or Grav pistol.
- Your leader is your only long range weapon. Consider adding a Lasgun or Autogun Ghost. They won't be "dangerous", but they can lay down some supporting fire.
- Long Rifles are "fine", but I've never been super impressed with them. I tend to put one on a Specialist Ghost if I want to keep them cheap and give my leader a spicier gun. A Grav gun with overwatch is pretty dirty

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- If you need more credits, consider downgrading your Nacht-Ghul to the Shiver Sword. While not the elite murder machine that is the Claw Ghul, it excels at punishing out-of-position gangers and juves.
- Whisper Merchants are nice and will pay for themselves, but if you need those credits for boys and toys consider dropping them.
With Delaque it's pretty easy to overspend on weapons, and part of the trick is finding the balance of boys to toys with your starting credits. That said I'm hardly the authority on Delaque, but I try my best

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Was there something in particular you were having trouble with?