When Shiro summons the unlimited blade works if he brings another person along with him could they wield his projections?
The weapons in UBW exist there physically, so technically anyone could pick them up and use them. BUT, a Noble Phantasm, as the crystallization of a legend, can't be wielded freely by anyone other than the original owner. When Shirou Traces Caliburn in the Fate route, he couldn't unleash its power until Artoria wielded it along himself. Projection Magic can trace the memories of the weapon so a proficient user (which Shirou isn't in said route) would get some proficiency with the weapon
Like in HF, when Shirou traces Heracles' stone sword and uses Nine Lives Blade Works
But normally, unless you had an NP like Lancelot's Knight of Owner, which allows him to use anything he recognizes as a weapon as his NP, you wouldn't be able to use another's NP properly.
There's special cases like Astolfo using Akhilleus Cosmos in Apocrypha, but that's because Achilles has himself lending away his arms and armor as part of his legend and Astolfo receiving weapons from others as part of his.