I use a lot of leather and care for it over the years, though I use cotton tape on my bars. In my experience, properly oiled leather grips everything better than dry leather, to itself, to steel, wood, hands, feet, whatever. So you idea to pre-oil is sound. If I were installing those on my bars (which I'd love to do, by the way! great gift!) I would also pre-stretch -- after oiling, stand on one end with your foot, and pull (harder for thicker leather). Then, as you wrap the bars, pull very snug at each wrap to get it good and snug. I wouldn't wait for it to get "dry," you want the leather to always be soft and supple.
I recommend Obenauf's heavy duty LP over their lighter oil. It will protect against sweat and sun better.
With abandon,
Patrick