Well, obviously this API has some serious flaws.
But if you use https, the URLs of GET requests will get encrypted along the way. (But still get logged in the cache of your browser. do clear it.)
So if you really like snipt, you could use a new twitter account created simply for the purpose of authenticating to snipt.
It won't feel particularly good. And I have some serious doubts about the rest of their security code based on this part of the API. But I do not see how exactly your credentials could be stolen using this part of it by others than the snipt maintainers who already have access to your snipts. So if you protect only snipts with the credentials, and no tweets, you should be alright.