This had been going so well until now.
Tuvok considers his options. Ultimately, he's unwilling to have a member of the security team carrying around a sword. There are several reasons. First, he's extremely skeptical that Mr. Laurence is correct that a sword could be more useful than a phaser in any combat scenario. Second, a sword is fundamentally a lethal weapon. A phaser makes incapacitation just as easy as killing, which hugely reduces unwanted enemy fatalities. Third, Starfleet doctrine is not designed to accommodate a sword-user, and re-training the rest of the security team doesn't merit consideration.
He has a brief impulse to dismiss Mr. Laurence on the spot. Upon reflection, however, he decides that that would be unwise. A preference to use the methods one has trained extensively with, that one knows one can rely upon, may be logical. Tuvok does not, really, think it is logical in this case. But a fundamental requirement of working with humans is accepting that they are not always logical. There would be no Federation if Vulcans couldn't learn that tolerance.
(This last part is an automatic mental motion that requires barely any time for Tuvok: he's been working with humans for a long time.)