Dear Pap,
Depending on the wading shoe a shoemaker might be the best choice for replacing the soles, especially if the felts are stitched to the last of the shoe. They can remove the old soles and re-attach them so they last.
If you want to do them yourself on most wading shoes it's not difficult. There are re-soling kits available at most fly shops. You can add studded soles when you replace your old ones if you want.
You need to start with clean and dry shoes. You need to remove the old soles and prepare the bottom of the shoe for gluing on the new sole. If the sole isn't stitched on you can just cut and pull it off if you take your time.
Once the old soles are off you will need to rough up the bottom of the shoe making sure you get the old glue off. Course sandpaper on a block of 2X4 will do that. Once the old glue is off you want to stuff the shoes with newspaper. Make sure you pack the newspaper in as tight as you can pack it.
Rough trim the new soles by holding them up to the shoe and trimming them with an X-Acto knife or a safety razor. Leave a little extra felt around the edges, you can always trim it later.
After you do that all you need to do is spread Barge Cement or some other waterproof contact cement on both the bottom of the shoe and the top surface of the new sole. Let it dry until it's tacky and press them on. Hitting the soles lightly with a hammer helps to make sure you get a clean glue bond across the entire sole.
Wrap the sole on with a couple wraps of Saran wrap and then duct tape the soles tightly to the shoe. Set them aside for a day or two in your garage to dry.
Once they are dry you can finish trimming the soles so they match the shape of the shoes and you'll be good to go.
Regards,
Tim Murphy 🙂