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Leather soles are heavy. If the shoe construction originally had stitching it's probably because it needs it.
You can ask a cobbler to do a blake/moccasin welt stitch (or words to that effect), rather than a Goodyear. Then it stitches inside the shoe, not along the outer welt. This isn't ideal if the shoe is the wrong construction and you'll probably be told "no" or "it won't work" .
Alternative is the leather is pinned down all the way with nails, super expensive if you want a fine job. Try find an old man cos it's not a common technique now, labour intensive.
pdlouche-
No stitches or nails that I can see originally, so it's been done either entirely with glue, or by using a hidden channel. I have been hunting for an 'old man' as you put it, but everywhere I have enquired so far just seems to be tooled up for doing straight swaps on shoes with a Goodyear welt.
Someone else told me a place called Tony's heel bar are quite handy, so will look them up too.
lmamammal
Yes, they are rather comfortable, worn barefoot most of the time ;)
I would just like to give them a new pair of soles so I can carry on battering them, they're for going on nights out, getting wet, dirty, etc. Not for wearing to an office, have other shoes for that purpose.
Problem is finding somewhere that can attach it without either using stitching, or it being visible.