The fragment of a URL is not sent to the server, so that’s where such platforms usually store the key. That’s also the way cryptpad does it. You can thus share the URL and with it the key.
Of course, you still need to trust the platform. The sourcecode link at the bottom of the page links to https://github.com/timvisee/send who forked from mozilla/send and links back to the web page.
I just use ansible to generate all wireguard configs and deploy them. Works great, but then, all my devices have static ips.