[/i]I have 450k on Morgan over-muscled Rover Plus 8. 375k of that on wire wheels, one with adapters (MWS) and another on MMC wire wheels and the last set (24 years) on a MMC test set of all-ss. [i]They seem virtually bullet proof. .

Add to that my wife's e-type on a Dayton set set of wires (chrome with ss spokes). Never thought about grease much. I just keep a tub of generic wheel and bearing grease in my garage. But I imagine any grease that is unwise to use, will cause damage. Unless required for some reason, I now remove, clean, re-grease and re-torque all my wheels and wires once a year. They are tight enough before this process. No problem with this since lessons learned. Read on.
BTW, I worry that if looseness is detected, even once a year, damage is already done. 
There is only so much grease can do, even the right one.
In my sad beginning, I followed the advice of MWS to the letter. Consequently, my first set of Morgan wires and the Jag's were soon ruined, requiring new adapters and wheels. And bad spline disease transfers from wheels to adapters/hub and vice versa.
https://www.mossmotoring.com/wp-content/uploads/2012/04/980-222-1.jpgThen I received from advice from a Morgan owner (4) who also owns an old Ferrari. Ferrari, and other Italian performance car racers, popularized wire wheels, which British sports car made their icon. My wife adores them They are much lighter than steel wheels and this was the pre-alloy era. They can also be re-trued track side. He torqued his wires to 250-300 psi, not to MWS 75psi. They will tell you that the spinners self-tighten. That is true but not sufficiently. After I began torquing to a la Ferrari and that crowd, I haven't had needed much wire wheel maintenance since or a need to regularly buy a new set of adapters/hubs or wheels.
Lorne
P.S. BTW, one can buy bolt-on wire wheels. Very hard to tell the difference unless what looks closely. They are extremely practical and save the high weight of adapters.
A little too practical for me. But we must ask ourselves a wire wheel question. Do we want them because of their sublime looks or because we like having the ability to tune them trackside like Ferrari did?