Certainly, there is no risk in using what fluke recommends. Barring that being a convenient option, I would recommend silicone dielectric grease.
In my opinion, there is no issue with it getting between conductors. As previously mentioned, there is sufficient contact pressure to displace the grease. What little will remain will be so fine in cross section, it will fail to insulate the contacts. And as it is non-conductive, and (generally) displaces water, there is no issue with it getting where you don't want it. If you need to solder in that location later, you'll need to clean aggressively with strong isopropyl, as silicone is the ultimate contaminant.
Don't forget, non-conductive just means high resistance, which equals electrical resistivity per length, multiplied by length of specimen (thickness seems more logical here), divided by cross sectional area of specimen (Pouillet's Law). So, imagine a glob of grease between the contacts, and surrounding them. The electrons must flow through the grease. There is a path directly between that has a small cross section, but a very small length (the numerator in the equation, making the resulting resistivity very small and therefore, sufficiently conductive to break down from even a small voltage). There is also a path through the glob, which is a greater risk, as it contacts other terminals. But, this glob has a length (thickness) orders of magnitude larger, so despite the larger cross sectional area, has high resistance, preventing spurious signals from getting through.
In my neighborhood, the most convenient way to get it is at the auto parts store, where it is sold as silicone dielectric grease or tune-up grease. I just looked in my tool bag, and the here is what I'm currently using:
Permatex, part number 22058.
Regards,
Mike O'