Yes, you can get a chamber reamer with replaceable bore pilot bushings to fit that .307 bore. European .308 Winchester/7.62 NATO rifle bores are about 0.001" tighter than US standard .300 bores.
However, the 7.5 Swiss may not use a .300" bore, which presents another problem: if the bore size is not a +/- standard size, you would have to have a custom bushing ground. Expensive. Plus, the 7.5 Swiss may not be readily available as a rental reamer.
As for doing it at home, unless the .308 Win and 7.5 Swiss chambers are really dimensionally close (and they probably aren't), you can't do acceptable rechambering without a lathe. A drill press or hand-held drill will not work. The final hand-reaming of a chamber is strictly for removing the final few thousandths of an inch for perfect headpace adjustment.
HTH
John