This really comes down to once again an argument about what exactly you are doing with the Bonus Action to cause the sword to reappear.

Consider this scenario: A magical cloud exists that shoots lightning bolts at wherever I point my finger. Is me pointing my finger a magical effect upon myself? Intrinsically? No; the cloud could just be capable of observing this, rather than anything magical on my part. Now replace the specifics of pointing my finger with instead 'use a bonus action' to cause the cloud to shoot a lightning bolt at a target of your choice.

The case here could just as easily be that the sword is capable of observing whatever the Bonus Action is - a hand gesture, a word, a flick of your hair, whatever - and then the sword uses magical means to appear in response.

However, I do find the 'Range: Self' argument to be compelling that at least in this case some magical link is present. If it had been 'Range: Touch' as per Goodberry then I would consider differently. Since Dispel Magic then specifically goes on to say 'Any spell of 3rd level or lower on the target ends' rather than 'Any effect of a spell 3rd level or lower on the target ends', then Shadow Blade would disappear in its entirety because the whole spell goes poof - otherwise, I would argue for ending specifically the ability to make the sword appear after being dropped or thrown.