As you probably know the capacitor acts as a spark suppressor - you might consider removing the capacitor from the new and fitting it to the original - if you're capable of soldering - and clean the contacts with sandpaper - they'll be blackened with soot.
There will be power going in and power going out - in between a centrifugal governor that switches the power on and off with the capacitor across the contacts.
I last messed with one of these in the 1980s and my memory is weak - but if you just go ahead and connect up as you see best it will either work or not work - the worst that can happen is to blow the fuse of the power circuit - you will not be able to damage the machine if you get the wiring wrong.
Have confidence
There are videos on YouTube.
Good Luck...
March 2016
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