I'm sure you know that the ArcGIS platform is ubiquitous in many industries so the concept of an "unrelated field" is quickly diminishing. A GIS certification is a great goal to validate your skills learned through Esri's e-learning web courses. The Esri Technical Certification program offers many certifications, but the ArcGIS Desktop Entry exam would probably be the best for you to validate your new skills. Feel free to engage with us on our new GeoNet space.
COGS requires a geography degree as a prerequisite to their 2 semester program, but they're flexible. If you're a programmer it shouldn't be a problem there.