When I've come across this problem and there is enough wood to allow a
person to do this, I simply pass the pieces of wood through my jointer.
Or sometimes I will take a thin shaving off with a table saw.

I always use a metal detector (a nail-finding stud detector works well
here) on the wood before I use any power tools on it as a tack or nail
can ruin the blades.  I most cases the blades spin fast enough that
they don't clog up, and you're left with a clean surface to work from.

Carbide tip blades will not dull with glue but they will chip if you
hit square nails.

You might not want to use this technique with a fine piece of woodwork
but it works well on stuff covered in contact cement paints and old
glues and gunky battered up parts.

Nelson E. Denton