I would say "How can I put this?...hmmm.." because you are looking for a possible way to say something gently. "How do I put this?" means there is a normal way to do it... I don't think that's really true, and.. "How shall I .." means "How will I.." ("shall" really isn't common except in the south of England, in my experience - most people think it's funny/posh) like you are thinking/trying to decide. That means you are telling the person "I'm trying to trick you by finding a way to say something bad, gently!" ha ha

"how do I put this" should suffice if you really have no idea how to express that thought, and "how shall I put it" is perfectly a good sentence to be used when you think you are going to say something that is honest but may sound rude, For example: "How shall I put it?/let me put it this way, he’s rich, but he’s certainly not attractive". but I am not a native speaker so let's wait for the opinions of native English speaker.