The only grease i saw in good meter where between the dial and the case, never saw anything on the pcb, even if you use some dieletric insulated grease it may provide a way to arc / spark
Humidity can cause some problems too unless you go for very specialised electrician meters DONT put anything on the traces pads, be sure to clean them properly with no residue left.
I tried on an Fluke 83 because the damn meter was acting strange, my biggest error. It was doing worse after that, had to use very specialised cleaners to remove it, was acting normally after a good clean up.
My other 83 began to do the same thing, a good cleanup restored it fine.
If your stubborn 001 DO IT and see what it will do and dont go over 300v, if it was good in some ways we should see meters with grease in them and as i see it its not the case on any meter i have or had in the past, i have all tear them appart.
You can do your own search ?
Finally i work in rf equipment, if we have anything greassy on the pcb, it fuck all the adjustments to some degree, instabilities ... it does some kind of capacitor effects on the tests points loll etc ... a very good clean up restore stability and effectiveness.
The grease maybe good in DC, but for Ac voltages and rf rejections up to 100khz in most modern meters i would be curious to see some tests.
And finally any greassy stuff may or will attrack dust ... more problems to come ?