WebGL and saved game data

I tried to find the answer

I released my game for PC, but someone suggested that because it is a smaller game, I should try a WebGL version.

If the original game has the saved game going to the persistent data path, what specifically will I have to do other than building it for WebGL. will my current save game system automatically store it to the browser cache and make the game playable/saveable without any changes to my PC build save system?

It will not work just out of the box. Without knowledge of your save system you should take a look how to store info in the browser IndexDB maybe.

Maybe you can try using browser cookies, or make your own server to save data using a mySql database and some php scripts