My first tinkering with anything FM

A further note: 
If it is an RF choke you have to replace then that is a somewhat less critical part (untuned), and you may not need do a realignment of the front end (RF-Mixer-Oscillator) coils. You need to determine whether it is a tuned circuit (RF, Mixer, Oscillator coil) or an RF choke. They could look about the same at 100 mHz. Otherwise, just try to make a duplicate of the original coil.
Rod

As before, you will probably have to make one for it out of some appropriately sized magnet/coil wire. Just make a duplicate of it except with leads long enough to fit the radio hookup or PC board. Be sure to scrape the insulation off the ends of the leads (and tin them with some solder) before you try to solder it in.

On second thought, you might find a prewound substitute coil (that could work) by looking over (all) the small coils available from sellers on eBay or elsewhere. One of these might have an adjustable core that would help with doing the alignment job. They will be small-on the order of the original, but on a plastic form for PC board use. These are fairly common. You could adapt one as needed for your radio set.

I think making one of your own coils would be best though-you'll just need some wire for the project and something to wind it on like a pencil or pen.

Thanks Rod. On further inspection, it probably is the RF COIL as the schematic identifies it as there is a nearly identical component close-by which I believe to be the RF CHOKE. Again, in my ignorance, I clipped the leads close to body so as to fishhook its replacement. So, is a replacement/substitute available?

Yes. The RF or Oscillator coils for a VHF (FM Broadcast band) radio will be physically small in size. They are often waxed (in a solid state Japanese radio especially) after tuning so they will hold their shape. These small coils are squeezed or expanded during the tuning (alignment) process to get them on the right frequency. Then waxed. So you might have to make up a new oscillator coil from scratch. This isn't that hard to do. Use some enameled magnet wire close to the same size wire if possible. Use the alignment trick I mentioned above to get it on frequency according to the dial on you radio. Good luck.
73, Rod  WB6FBF

An Olympic 7-532w is my 3rd radio restoration. In my enthusiasm to cut away all paper caps, I clipped something loose that looked like like a small cap with melted wax. Upon further inspection, I discovered that inside the thing were windings visible through the wax. This thing was as small as a resistor and came from the "FM side" of the circuitry per schematic. After cutting and then looking at the schematic (stupid I know) I realized that it is PROBABLY the oscillator coil. There are a couple of question here that I hope you can help me with. Were the FM oscillator coils on these sets as small as a resistor? And if they were, can a replacement even be found?