Mapleshaderecords.com
offers a unique item,
"Clearview Double Helix Power Cord Kit" that you splice onto your chopped short (by brave you) existing pigtail of a permanently attached power cord.
You can call or email the company to find out the real world results of this idea which lets a bit of the original puny vintage cord remain.
I use their power cords and power strips, but never had the courage to chop short a built in AC cord, although none of my permanently attached cords are as rudimentary or needy as what you describe.