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Blimey - 5/64ths is so close to 1/16th that there isn't an issue - 1/16th rod is so commonly available!

Ignore the tiny extra 1/64th of an inch and say it is 4/64ths for a sec, that's the same as...

5/32nds is fairly common for old razors like these - you find that size in the centre of the big, ornate bosses of some very early razors too, sometimes brass, sometimes copper, sometimes plain iron....