Wooden shoulder planes?

They work. They are lighter than metal planes so they will
have more of a tendency to chatter when cutting end grain
in firmer woods. Keeping the iron very sharp and setting it
for a fine cut improves performance. Same for metal planes.

More concentrated mass equals more control in my experience
with shoulder planes.

The shoulder of a tenon is the end grain left from what’s cut away to create the tenon. Shoulder planes are low angle planes to handle this end grain. Shoulder planes are usually bedded at 12º or 20º and wooden plane bodies tend to fail at these low angles because the pressure of the wedge is so close to the natural cleavage failure nature of the wood’s grain. I do have a commercially produced British boxwood shoulder plane and it has an old split just as I’d expect.

If you’re thinking of adjusting tenon thickness by planing the face of a tenon, a shoulder plane is probably not the best choice. For that you’d want a rabbet plane pitched appropriately for the wood you’re working.