You're not asking for input on whether or not you should take it, so I'm not going to provide that input.
Instead, I'll simply answer your question as you posed it.
So what should you say? Well, it doesn't actually matter.
Could this negatively affect how your superiors view you? Maybe, yeah.
Could it hurt your potential upward mobility in the future? Maybe, yeah.
Could your boss take this as a personal insult? Maybe, yeah.
Do you really think that specific phrasing can actually influence any of those things? Lol, no, you don't have that power.
Keep it simple, just say that you won't be applying. Explain as little as humanly possible, and if you are pushed to give any kind of reason, then stick to something vague like "bad timing".
They want you in the role. If it's an easy role to fill, they probably won't give a shit if you aren't interested. If it's a hard role to fill, they might get butt hurt that you reject the opportunity. At the end of the day, their opinion of you will be based *almost entirely* on how inconvenient your decision is for them.
So don't over think it, and keep your answer as simple as possible.