Do the legs seem to be weak at all?
Any in-coordination, or stumbling?
Have you checked him for fleas?
Leg shaking is not a typical sign of arthritis. (Though I won't say its impossible.) What I have heard of is pets experiencing leg numbness, itchiness, and neurological symptoms from over the counter topical flea products such as biospot. Here is a link to a page with one story:
The ones you can purchase from your veterinarian, such as Revolution, while not 100% safe, are MUCH safer than the other options.
If he should develop any other symptoms, such as lethargy, loss of appetite, or in-coordination then I would recommend a visit to your veterinarian right away.
If you have further questions let me know. If this answer is helpful please click accept. Thank you.
The fact that you just put it on him makes it even more likely that the Biospot is what's causing the problem. I would recommend bathing him if he will tolerate it. Then as you said above, I would use Revolution for next month's treatment, and visit a vet if this persists.
I don't know that he's in pain, but you are right there's not really any way to know that for sure because cats hide it. I think its likely causing itchiness or numbness so that the legs feel strange to him, and that's why he's shaking them.
You're welcome! (Sorry for the delay.)