Why do you need hole signs at all? In particular at a private course? . . .
You don't -- we don't. Took them out eight years ago.
However, our course is compact and open. If you don't know the sequence, there are a number of places you could go wrong. For outsider tournaments and outings we used to spray some sort of disappearing "paint" next to the tee boxes to indicate hole numbers. Recently I think we've gone to very small (like 8" x 10") white cardboard signs stuck in the ground for the day. The only thing on these signs is the hole number. For the occasional unaccompanied visitor(s) we have little course maps we can give them. Hole yardage is on our score cards.
Several years ago we had a state golf association tournament and they brought in put up their own large hole signs with the association logo and typical assorted information on them. The signs were heavy duty with nice graphics. However, the overall look was ugly and really made me appreciate the clean no-sign look.
By the way we, don't have ball washers at the tee boxes either. We took them out around 8 years ago (at the same time we removed our old tee area signs). Some folks complained at the time, but I don't hear any regrets now.