Getting the PEX pipes into the coop without drilling holes in the walls was the goal. My solution was to use my angle grinder to cut flaps in the wye fitting outside the coop and in the air duct inside the coop, before the intake fan.
The cutting went pretty smoothly. Fortunately, the wye fitting had a wide, flat space between the two legs. The longest cut had to be made at an angle, rather than perpendicular to the surface, but it worked well enough. I was concerned with breaking the cutoff disc so I was careful to keep the force directed radially, as much as possible.
The cold PEX pipes were too stiff to conveniently bend through both openings at once. The solution was to slip the wye fitting over the pipes, all the way to the opening of the corrugated ventilation pipe, then feed the PEX pipes into the air duct, through the opening, into the coop. As the wye fitting got closer to the air duct, it became another wrestling match. Fortunately, I only had to wrestle it for the last foot, or so.
I was able to hold the pipe bundle between my knees, hold the fittings to gather with my left hand, and use the drill or screwdriver with my right hand to make the final connections outside the coop. I left the duct tape indoors until it was needed. Keeping it warm made it simpler to seal up the insulation and plastic sheathing around the pipes.