Here's my question: If I'm not in the mood, what is the best way to approach it so that my partner isn't hurt?
Well, you could always lie, you know. Try to pretend that your rejection is not really rejection. That your rejection is not something that you do, but something that is coming from the outside - some independent external circumstance and not your personal choice born of your own free will and decision. You can always make an excuse about being tired, being traumatized by something you didn't even bother to communicate, etc. You can promise that you'll do it another time with the full understanding that you're not really intending to follow through with that promise. Make an empty promise. You could lie that you really do still love him, you really do still find him attractive and sexy, but some unknown vague undefined outside force is preventing you from being with him, even though you would absolutely love to you just can't.
You can try all of the tricks and you probably already do. But your partner will still see the rejection for what it is. And he will listen to your lies and excuses and still see through them at the reality that you no longer love him. And no amount of lying, making empty promises and giving the best possible reasons will ever help you.
Cause it doesn't matter. Bottom line is you are choosing to reject him. That's what's hurtful. There are no magical words that will convince him that the rejection you're choosing is what he wants.
it's best not to rush back into the physical
That's another great one. Keep pretending that you were going to rush into the physical, as if that was ever true.... At least for a little while you may fool him that you were totally going to have sex with him but gosh darn it something was in the way, stopping you despite your determination to have sex.
Truth is you failed at this relationship. And now you're looking for ways to continue failing, but in a "nicer" and more efficient way. I really don't understand exactly what it is that you think you're bringing to this relationship, but you are gravely mistaken.
A good partner will ask questions like "How can I make my SO the happiest?" and you are asking questions about "How can I reject my partner and feel good about it too". Kind of tells you all you need to know about your current situation.