Hey, sorry for late response.
I've got a websocket server for Kelp available on CPAN:
https://metacpan.org/pod/Kelp::Module::WebSocket::AnyEvent . It is really a standalone AnyEvent WebSocket server that is nicely integrated with Kelp via my another module, Symbiosis. Unfortunately it requires AnyEvent non-blocking server, for example Twiggy which is stable but not currently maintained (and I don't know of any alternatives).
If you want to have a better support for websockets, you're better off using Mojolicious. Fortunately it is extremely similar to Kelp so the transition should be relatively painless.