There is a way to do it that is a bit of a hack:
Create a keyframe for your shape layer path.
Cut that keyframe
Open Illustrator and paste it into a new document
Apply a stroke color and adjust the stroke’s tapering to your liking
Expand the appearance of the stroke
Copy that object from illustrator
Create a new Solid above your original Shape layer in AE
Paste the Illustrator object onto your Solid
Use that Solid layer (That now has your Illustrator Object as a mask channel) as a Track Matte