Gillette Slim Handle Adjustable 1-9 Razor
In the 1964 movie Goldfinger, we get a close look at Bond's shaving gear. He uses a Gillette slim handle adjustable razor when he is shaving in Goldfinger's plane on the way to America. In the handle of the razor he has hidden the tracking device. After unscrewing the bottom part of the handle, he takes out the device, activates it and puts it in the hidden part of the heel of his shoe. Now that's a pretty cool 1960s spy gadget sequence that the modern Bond films can take an example of.
The Gillette Slim Adjustable 1-9 razor is still easy to find on eBay (see below for the most recent offerings). Make sure to look for nice clean examples with original cases and paperwork. The online shaving store The Executive Shaving Company usually has a few of these original 1960s razors in stock as well (see their current Vintage Gillette Slim listings).
Thanks to Luka for the alert
Other times we see Bond shave include the movies Live And Let Die (Schick injector razor with Schick lather shaving cream), Die Another Day (Norelco/Philips shaver) and SkyFall (razor, brush, wooden bowl).