Even better than the WD40 silicon lubricant in resisting fingerprint smudges and grime is this leather conditioner that I am using. It repels water and resist fingerprints...to put it simply, it provide an oleophobic hydro layer. It is not cheap, it cost about S$19+. I used it to condition my leather home theater recliner.
I have been using it for about a week now and there is a significant reduction in fingerprint smudges. There will still be fingerprint if you have sweaty palms, dirt and grime but it is lesser smudgy and easier to clean with a microfibre cloth. Pls apply on the outer screen (and any tempered glass screen protector). Do not apply on your inner screen.
Of course, some will go the extent of using car wax which has the same effect. But if you are concerned that car-based wax is too strong and corrosive over time, you may want to give this a try. If it doesn't work, at least you can use it for your leather seats (which is the correct application anyways)