Supermodels seem to like beards these days, or at least every commercial and magazine seems to depict.
That said, if I needed the closest shave with no chance of nicks, cuts or skin bumps, I’d have to use either my British Goodwill or my 1934 Aristocrat.
For tactile pleasure, I'd choose my Robert Wade straight, made around 1815, as I get a buzz out of the history aspect of shaving with older implements but as this is the DE forum and my straight shaving skills are far from honed (see what I did there? ), I think I would choose my R41 for the closest shave and a Gillette Slim for comfort and coolness. I've used Slims more than any other type of razor since I started with DEs 4 years ago so I'm more familiar with them. Also, I'm a big child so the fact I have a 1964 Slim makes me feel like James Bond when I'm shaving (it's also why I hope I'll enjoy the L-type Schick Injector that's on it's way to me from Canada right now).
No shave. I would not dare to use any of my razors as my wife (who is both a medical doctor and exceptionally cunning) would have smeared all my Feather blades with deadly poison - and I probably would be so excited that I would cut myself, even with my AS-D2...
I read the OP wrong - I thought the supermodel we had a date with was our best razor! If I had a date with an actual supermodel, I’d probably be too nervous to shave.
Just one? I'd do first two passes with GEM Micromatic Open Comb (ATT SE1 a close second-ran). Next two with Wolfman OC .74 (Timelss .95 also-ran here) Clean up sideways around the Adam's Apple with a Schick Type E .. then touch up after a rinse with ..
Of course by then I'd probably expired due to old age ..