DYIMAN, a basic rule of plumbing is that you never, ever, double trap a fixture. The result would be that the drain would become “air-bound” and would drain very poorly.
Since you do not have the clearance to offset the drain, your best option is to do what you obviously don’t want to do: cut the copper and extend the p-trap to the new shower drain. If there are other fittings involved, it becomes more complicated, but if you are a real do-it-yourselfer, you should be able to handle it, assuming that you can handle sweating copper.
A simpler alternative to sweating the copper is to buy some clamps and PVC at your hardware store, but it would not make nearly as good a job, and I am sure that you want this to be lasting and leak-free.