I'm replacing the electrolytic caps on a CRT from the late 70's early 80's. The PCB has about 8 caps in total. From the schematic, the
Horizontal Deflection cap is a 16uF 63V Bipolar. I ordered a 10uF 63V B.P. off Digi-Key since they did not have a 16uF and that was the closest and from what I read, someone else used a 10uF with no problems.

When my package arrived, this cap is significantly smaller than the original in both diameter and height. I would say about 1/5 in size. Has the size in capacitors shrunk that much in 40 years? Or did I order the wrong cap?

 

Yes, they have shrunk a lot in the last 40 years. One thing to which one should pay special attention when replacing capacitors in and around the horizontal deflection and high voltage circuits are the current ratings of the capacitors. Get an idea of the RMS current and then make sure the capacitor is rated to at least 130% of that current taking frequency into account. Otherwise you might be replacing it again shortly.