Great birthday present! And happy 60th!
As above, I would just clean and dry it with loo paper, try to avoid getting water in the scales and pin, and in any case a wipe between the scales is good. I strop my straights perhaps 30 laps after a shave and 30 before. It seems less onerous than doing 50-odd before the shave, and ensures its clean, dry and essentially ready for the next day.
If you really want to use something on it, perhaps before extended storage, you can get Clippercide, which is like a mix of Barbicide disinfectant and clipper oil. But unless you live near the coast where rust taps you on the shoulder, you can probably just keep it clean and dry without the extra products.