I find the waviness thing varies greatly from my limited experience. I've had a couple that were very clean and hardly any problem and I had a couple that had more hammer/grind ripples than you'd find waves in the ocean. I wonder if it isn't a matter of some swords being done by more experienced smiths and some not, being in a factory production type manufacture....

The Towton sure enough looks like a nice sword. I find it tempting, certainly...