Or you could simply use a router that was intended to do such a thing, like the Festool mfk700. It makes this job as easy/safe and dust free as possible.
I worked around this problem for years with different methods and varying degrees of success. An offset fence on a router table works well, but only one smaller parts like shelves and it can't do curved pieces at all. Block planes and card scrapers work too, but they are tedious and slow, not a huge issue to a hobbyist but not when you do it for a living.
Lamello also makes a "lipping planer" that does a fine job, but it is a strictly dedicated tool, that's all it does. The mfk700 has vertical base options that make it far more versatile.