Which stylus is correct for a Shellac LP

Yes you should use the correct stylus !
https://www.lpgear.com/category/78STYL.html

... and that would be?!

Here ya go!
https://www.lpgear.com/category/78RPM.html

OMG.  I have a stylus for my 78s, and I have a stylus for my LPs (33 1/3).  The question is: are the grooves on the *shellac LPs* wide (like they are on 78s) or narrow (like they are on LPs). Did the recording process affect the grooves (utilize or create narrow grooves) when they made shellac LPs?    

+1 Elizabeth! I have an early Sonny Rollins pressing just like that in mono from the early 50's. Same groove width as all LPs.

The groove width of a 78 compared to a 33 and 1/3 LP is readily apparent to the eye! No need for a magnifying glass!

"The eye" is relative, (or at least mine is no longer that objective), but I take the reasonable explanations offered - thank you!  I only asked in the first place because I was always taught the rule of thumb: Stiff = Shellac and 'Bendy' = Vinyl.  I actually have a quite a few stiff LPs.  Do I now I have to worry about using a mono stylus for those playbacks instead of the 2 channel stylus I normally use? 

There were 78s recorded with the 'microgroove' process. They are very much the exception! And they will say 'microgroove' on the label.
All LPs use the microgroove stylus as Elizabeth pointed out.

Not a "purist" - (I assume you mean a mono cartridge, etc., for mono LPs) - although I probably would be if I could afford to be.  I just want to protect the equipment and platters, and it sounds like I can proceed with what I have.  Thanks, again.  Micro-groovy!

harrar, at the very least a mono switch may provide quieter playback with mono LPs if you can't afford a separate mono cartridge.

The value of this may be argued but not all "mono" cartridges are true mono, some may be strapped internally.  You can do that yourself if you have a second cartridge you may not use as much (instructions found online).  A second tonearm is not necessary either if you have an interchangeable headshell arm.