Lastly, you will need a "V-Dapter". This time I am recomending a particular brand product, as it is the only one that I know of that attaches by screwing on by the cable clamping bolt mentioned earlier. All others I've seen slip into the yolk where the u-tube usually goes. Standard cantilevers don't have this yolk!
If you want to add a cable adjusting screw, drill out the hole in the "V-Dapter" which goes through only one thickness of metal. The other hole is for clamping it to the brake. Drill it out to 1/4". Don't bother to thread it, there isn't enough metal. Use the locknut to adjust cable tension.

If you bought new brakes, attach them to the bike and adjust them so the brake pads contact the rims properly. Now attach the "V-Dapter to your standard cantilevers following the instructions that come with them. You can now throw away the straddle cables, cable anchors, and, If they aren't a part of the frame, the housing stops (hangers). They are just dead weight. In fact, since your "W" brakes are smaller than true "V" brakes, they are lighter than the full sized models!

However, be warned! These brakes require less cable pull than full sized direct-pull canti's, plus they have the additional pull suplied by the "V-Dapter". And, if you used them, the non-compression housings suckup less brake energy. So be carefull when you first try them out. They will be MUCH more responsive than your old method of cable routing! In fact, although you have to squeeze harder, theoreticaly they can supply MORE braking power than normal direct pull brakes using road levers. Because no matter how hard you try, you probably will not be able to squeeze the brake levers hard enough to touch the handle the handlebars.