I also got a BS in MechE, then got a job as a software engineer, so now my girlfriend wears my ethics ring. I guess we're exempt from programming morally!
I have a B.Sc. EE and yet work mostly in web/mobile software. I don't consider or present myself as a "practicing engineer" but I still wear the ring as a reminder of the obligation I have towards anything I create for other people to use. I probably wouldn't give it to my girlfriend to wear, but to each their own.
That said, if you've been obligated and are working in a technical field, but don't really consider yourself an 'engineer' you can still wear it, so long as you hold yourself to the values it represents.