Neat idea, I personally never used telegram but heard a lot of positive feedback about their ux. I only have a feeling that, at the protocol level, the two ecosystems might be too different to make it viable.
That’s just a feeling tho, so go for it.
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.