Once I trim 1/4″ on the side, it will slip into the narrower opening and have plenty of space on the side. A new pot is not an option. Will doing that definitely kill the Palm is my question.
Ponytail palms are pretty tough, so it's not for sure that cutting the side off will kill it. It will definitely increase the chance for disease though. If cutting one small area will allow the plant to slip inside the pot rather than perch on the top, and you don't feel you can use a different pot, and you're prepared for the possibility of losing the plant, then go ahead and cut it. Let us know how its doing a year from now.