Try some string and a toothpick. The toothpick will break easily. It'll still be strong enough to bring the blind nut to the hole.

Or, only bend the coathanger wire at just enough angle to keep the T-nut on the wire. When you bring the nut to the firewall and into it's hole, only a little effort will pull the coathanger on through.
Or simply push the wire carefully back into the fuselage. It'll fall out after you've managed to get the bolt threading into the blind nut.

Plan on the nut not wanting to stick into the hole. It fell out, after all.

My hands are small enough that I can get to the back of those nuts when they're loose and won't hold firmly. Just a finger pressed on the flange is usually enough to get the bolt started. Once it's started, pull the bolt head to seat the nut.

I usually place a dab of epoxy on these troublesome T-nuts. It's sticky enough to hold the sucker so the bolt can grab it. And you're going to need that glue to hold the thing next time something gets loose.