Despite the sometimes complicated outline, the part of the router bit that needs to be sharpened is actually flat. A few minutes work with the appropriate sharpening stone, and the job is done.
If you own a wood router and a collection of bits, you might already have what you need. The bit doesnt need to be purpose-made for planing. It just needs to cut a flat surface. I used the bit ...
On this show of the Router Workshop, Bob and Rick will show you the easy way to make an attractive panel door for any cabinet using your 1/4 straight bit, a 1/4" round over bit, 3/4" flat bottom ...