If you don't have the Bolt-Caster in your Exotic Weapon Blueprints, then yes, I'd buy another from Shaxx and infuse it up.
I've done all three quests, and helped a friend through getting his Bolt-Caster and Dark-Drinker on the same Sunless Cell run, so it is possible to do them simultaneously.
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I just bought a new Arc Edge, infused it to 310, upgraded it fully, and still have no quest from Shaxx. Thank you for the suggestion though!