No, you've distinguished between a magnet and a charge, which is quite a bit different from distinguishing thier fields
I'm thinking that an electric field interacts with an electric charge and a magnetic field interacts with a magnetic ... ?charge?. Since you need relative movement for crossover, it only matters if they're static. And since, in reality, nothing is static (except the 4D El_Mac, of course but I'll pretend that that's only relatively true), it doesn't matter.
Bah, this is tough to explain.
Trust me, the proton and electron would each change orientation by 90 degrees, and leave our 3D reality and go into their own separate ones. This would be a result of losing their field. The energy would 'kinda' come from losing their spin.
We're talking about an outrageous event here, so we need an outrageous answers.