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Varnish first to be thorough. A pipe cleaner is a useful tool for varnishing the insides of the holes for the cane. After you cut it, give the wire an extra twist to keep the fuzz from coming out.
For the inside of the holes in my seat frames I used a small piece of foam cut from a foam brush with a sandwich tie twisted around it. It held lots of varnish and did a great job.
Cheap, easy, effective. Just an idea...
Dave
"If given six hours to chop down a tree, spend the first four sharpening your ax." - Abraham Lincoln