Unfortunately, the Web Crypto API doesn't automatically get you safe cryptography either. It was added by the W3C to allow video vendors to implement content DRM in pure Javascript rather than requiring plugins, and so it includes a great deal of legacy crypto.
Long story short, you need an expert in cryptography to design this for you, whether or not you use WebCrypto.
This isn't something you should take risks with. It would be better to advertise a decentralized social network with NO CRYPTOGRAPHY (which is what this essentially is) than to say it has "cryptography that hasn't been audited" (which most users won't distinguish from real crypography).
Long story short, you need an expert in cryptography to design this for you, whether or not you use WebCrypto.
This isn't something you should take risks with. It would be better to advertise a decentralized social network with NO CRYPTOGRAPHY (which is what this essentially is) than to say it has "cryptography that hasn't been audited" (which most users won't distinguish from real crypography).