I've not had to do this to any of my AI Nikons with rings, they just have not been sticky(Nikkormat FT3, FM, FE2, EL2, F3).
On the Retina IIIS and on some of my fixed-lens cameras with aperture/shutter rings, and a Canon 50/1.4 RF lens- I apply a small amount on the outside of the ring. I would try that first on the Nikon AI ring, then work it a little. If it frees up, swab it with a Q-Tip. That worked on my Retina IIIS and a Konica S2, as well as the sticky Canon aperture ring.
I would not remove the lens mount unless you've got some experience assembling and disassembling cameras. The latter is always easier...