Insert jacks are wired for TRS cables, because in their traditional use, they're meant to both send and recieve a signal in the same jack/plug. If I remember correctly, I think the Tip is the Send, and the Ring is the Recieve.
So an "insert" cable will have one end with a TRS jack, and then two other ends with TS jacks.
So if I've got this right, if you plug a TRS or TS cable in one click, it will send to the Delta 44 without breaking the normal, and you will also get signal flow though the mixer.
If you plug a TRS or TS cable in all the way, you will send to the Delta, but the normal is broken, and it will interrupt the signal to the mixer.
So I'm not sure it matters all that much. If you don't need the signal to return through the mixer (and it sounds like you don't) you won't be making a balanced connection anyway, so you might as well just stick with TS cables.
Your other options are, depending on how many mics with phantom power you're running, and the capabilities of your mixer, you can just use a combination of bussing/panning and the mixer's regular outputs.
Or get a cheap stand-alone pre-amp with phantom power.
If I totally screwed all that up, someone correct me, it's been a while since i've used inserts for outputs.