The speedo cable is attached to the tail shaft on the trans and a slipping clutch should not affect it at all, the new cable could have sat on a shelf for a long time and the lube got hard. Clean the inner cable and spray some brake clean thru the outer cable, blow it out and relube it. Remove the speedo and blow it out gentle with low pressure, it could possibly have dust and crud inside it ( remember it is over 45 yrs old). Good luck.
