Making http stream to be https

I'm working on Alexa skill to stream some custom radio stations. The issue is that Amazon requires https for the stream but some of radios stream over http only. I'm considering what are options and would be glad if you know about some other options.

My list is

• Creating an https website that gets the original http stream and sends it over. This however seem costly. It'd be nice if there was such a website hosted by somebody
• I don't have much other ideas

(I should say that I'm not maintaining the radios so I can't influence the protocol they use.)