Depending on the situation and the relationship you have with Jim, saying "I'm not in a position to ask for that right now. Happy to help in other ways." might work.

Why not actually tell Jim the truth? Why not be open and honest? Anything else is being a bit of a douche, no?

I assume you would have a reason for declining the opportunity to make the introduction - help Jim to understand that.

Yes. If honest was the following, then it would be easy: "Hey Jim, I happy to make the intro. But I don't think it makes sense now. My mentor is really busy and this project is still too young for him to be interested." But what if being honest was this: "Hey Jim, I have a ton of huge doubts about your project. To be honest, the idea seems silly and I don't know if you have the skills to execute it. If I suggested that my mentor spend time coaching you, it would reflect poorly on me. It would appear that I was wasting his time. That said, I know little about your project and industry. And I don't have the time required (right now) to intimately understand you and your startup." Is something like that too harsh?

I'd be a little more diplomatic about the exact phrasing, but if that's how you feel, then Jim can seriously benefit from time with you. If the project has merit then a serious discussion with him about it will convince you, and then you can help him frame his approach to your mentor.

If it doesn't have merit, and you're right to be concerned, then you should be able to convince him of that. If you can't, then at least you can honestly say that you've got serious reservations about his project, and you're worried that introducing him to your mentor would reflect badly on you.

In effect, if that's how you feel then you should be the first phase mentor/advisor. If you really don't know much about his project and industry then you need either to (a) learn about it through him, allowing him to coach you, or (b) say that you don't know enough to know if Jim is a good fit with your mentor.

And if you really don't have time, then say all the above, and then say that your lack of time is the block to understanding his position well enough to make the introduction in all faith.

Is Jim really a friend? How can you best help him? Is that your aim, or are you just looking to brush him off as a bit of a distraction? If he is a friend, and you want to help him, and you really don't have time, look for a quid pro quo - see if there's something he can do for you to help you make the time to do something for him.