Assuming:
195/50R19 -- 26.7x7.7
195/60R17 -- 26.2x7.7
I leave the [fat tire-small rim]/[thin tire-big rim] debate to others.
Diameter is given, width is the same. The offset will affect how the tire sets in the wheelwell. Flush seems best, but poster Cd wonders about examples like Blowfish and other racers.
i.pinimg.com/736x/c7/ce/b8/c7ceb80bd139c38ef9218bcde2487821.jpg
I would put the rim width equal to or greater than the tread width.
i.imgur.com/Cdh4U9B.jpg
The wheel disk overlaps the tire bead to give the smoothest possible profile.