It's possible to install modern, wider tires on the old narrow rims, but they might crown (wear excessively in the center) and wander on the road. A modern tire of 6" tread width should be OK on a 4.5" rim tho.
Not saying wider tires can't be installed or won't work, they might just be less than optimal. However if you aren't driving it a whole bunch, it might not matter. Also a slightly crowned, modern steel belted radial will still handle so much better than the old bias tires that it will be worlds better.