Do I need new cork and is it possible to do only that?

I have a pair of factory seconds AE wingtips that I have worn the heck out of. For years they felt like extensions of my feet, but now they feel like blocks of wood. The outsoles are still in pretty good shape and the footbeds certainly don't look new but aren't torn; has the cork worn out/gotten compressed too much? Do they have to take the soles and heels off to fix this, and can the same soles and heels be put back on or do they need replacing?

Since people are saying the recrafting service isn't reliably amazing these days and I don't know that I want the uppers redone and these are seconds to start with (the sizing is way off what's marked on them) I'm more likely to look for a good local cobbler if my area still has any...

Thanks!