if you collect the fly, give it to the cat, click the cat, open the toolbox (if you clicked the respawned fly first thats ok, its just a visual glitch), kill the squash, open the door, luig
At any time, while your item slot is occupied (IE: with Gardening Shears or Key) and when you go back to the first room. You can pick up the fly again. And it'll replace the current item without no way to progressing after
