It seems reasonable to me.
From the look of things, you will have Electric Arc to use when Devise a Strategem rolls low, so that is handled.
There are many who list Investigator as a low power and difficult class to play. Though if you replaced the Champion with a Swashbuckler, I think you would have the full set of them. So lol. Have fun and enjoy.
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Looking at your group composition, you probably already have a face with the Champion (and maybe Witch), and Empiricism doesn't give you a whole lot to work with in regards to Charisma, though honestly having 3+ Intelligence-based characters is even more overkill. I probably would have given it a pass for Interrogation (and if you didn't have a character like the Champion in your party), but the Charisma seems like deadweight given that a majority of the Charisma stuff is covered in-party already. There's also the issue of having low Constitution and Wisdom, which affects HP, Fort Saves, Will Saves, and Perception (and likewise Initiative). While the former two aren't extremely crucial, they are a weakpoint in the class that should be shored up, and having not-so-good Perception is really painful for your group when trying to find traps and hidden doors/loot, since nobody else is going to have better Perception proficiencies and stats as you. Being able to do a Recall Knowledge check for free every 10 minutes on an enemy is pretty massive to help identify what tactics would work best on a given enemy, especially if you invest in the Recall Knowledge feats that Investigator has.
Having made an Investigator myself and ran him up to 13th level (and counting), I built him to have 18 Intelligence, 14 Dexterity, 14 Wisdom, 12 Constitution, 10 Charisma, and 10 Strength; having an Oracle and Tyrant Champion in the party, my need for Charisma was practically unneccessary. I run with a Shortbow combined with a Rapier back-up weapon, as well as a Starknife just in-case. My boosts always go to Intelligence, Dexterity, Wisdom, and Constitution.
If you're still set on going Charisma-based, I would just leave Constitution at 10, and put Charisma at 12, boosting it in place of Constitution when you can. If you're not, I'd add that you move Toughness to 11th level and take Fleet instead, since movement speed is almost a must-have for action economy effectiveness (having to waste another action for 5 feet is annoying).
I don't have much advice for Snarecrafting, because I've never seen it in play, but I would imagine that it requires some sort of set-up for it, meaning I wouldn't rely on this always working out in a combat situation, especially if the plan is to pluck away at the enemy from afar (since the Shortbow is basically the best Investigator weapon to have). Not to mention that not every enemy is going to just waltz right into snares you place (though I can understand using them as a means of battlefield control).
Do you plan to boost your Spellcasting fully? I would suggest it, since you'll have full Intelligence scaling, be only -2 from full spellcasters in the endgame, and you can get some pretty nifty spells that way, both for out-of-combat utility and in-combat buffs/debuffs. Even something as simple as Haste/Slow for pre-buffing would be massive for the party, since the Witch might not have access to these types of spells (depending on which tradition they take. Bonus points if they're non-Arcane, so you can boost Arcane to Legendary to add some skill versatility to the group).
Using save-based effects is fine in the early game, since you have the same Save DCs as any true spellcaster but later on, it's going to have serious diminishing returns, to the point that maybe risking a non-DAS strike would give you more DPR. By 7th level, you'll be at a worse proficiency than the Witch until you get Expert at 12th, then be worse again at 15th until you get Master at 18th, then be worse again from 19th onward. You also won't have access to the extremely powerful spells that a true spellcaster would have, though a good amount of them are still useful across every level of play.