The airlines do not take kindly to what you are contemplating. As pointed out upthread, there can be significant issues with any checked bags (whether checked at the counter, or gate-checked - yes, since you're in business class, you should be able to manage with carry-ons). Note the point above about in whose name the bags need to be checked. Remember, you would be treated as a no-show for that flight you plan to skip. For security, they won't load/will unload any bag you have checked.
There's one other possible wrinkle, although it's probably unlikely. Airlines hate when people do this. They sometimes take punitive action against those they catch. They typically don't take action unless they think someone is repeatedly abusing this, but in those cases they have confiscated all the offenders' frequent flyer miles, and even banned (for life) those who they have caught. Those are extreme measures and if you have an otherwise good record with Delta they probably wouldn't go there, but keep in mind there is a risk that they could make an example of you.
Given that it's company travel (they're paying for it, and they need you in Dusseldorf on short notice) I'd have your company's travel staff work it out, and eliminate any shenanigans you feel inclined to do. Personally, I'd hate to lose my stash of FF miles (and if you're flying in business to/from Europe all the time, you might have a large, valuable stash to consider) so I'd take reasonable measures to protect them.
Just how I'd approach it. Good luck.
