This prints with no supports, though a few bridges are required. The solder spool beam is a very tight fit through the back plate, but it should never be necessary to remove it again, so provided it's strong enough, you should be able to force it into place. I printed in ASA, due to the potential for contact with hot solder, tips, etc, and with 3 walls to support the weight of solder.

The three triangles are 0.2 mm apart in size, and used to keep the solder spool/solder wick from falling off the end of the beam. Try to insert them with the side from the print bed facing towards the soldering iron. This should be removable.

To install, remove the included solder holder, and reuse the screws to attach this. On my iron, the screws did not align easily. Turn them backwards until they catch the threads, and stick out straight, then tighten.

I designed it for the Engineer SS-02 solder sucker: https://www.amazon.com/dp/B002MJMXD4 but any with a diameter of 20 mm should fit.