KY would probably melt, not gooey enough.
I have seen attachments that will hook up to suction that sort of surrounds the bit, sort of like a collar that goes around it, which you then hook up to suction/shop vac.
Sort of like this one that is for a little sander, but might work okay. Clamps on, and attaches to shop vac using a hose.
https://www.dremel.com/en_US/products/-/show-product/accessories/mm830-dust-extraction-attachment