Thing is, you may not need grease. If you really want to take down the hub to examine the cones, you do need it.

Some sources say it's probably ok to put the cone wrenches on the cones and just loosen a slight amount.

That's instead of loosening a locknut, moving the cone back, and holding the cone while retightening the locknut.

If you go too far with the first method, put your crescent wrenches on the locknuts when you tighten.

be careful with how hard you turn the wrenches because it is possible the Shimano factory left the locknuts so tight that you'll ruin the threads. If they don't move with just some firm pressure, then don't use the simplified procedure.

Neither procedure actually requires fresh grease unless you back the cones out and wipe them off to look at them or unless you get some grit in there.

any good grease will probably do. It's probably not necessary to follow the stock advice to get waterproof boat trailer grease if your hub has rubber seals.