Yup
All you can do is to get a traditional “tune-up”, i.e.–replacing plugs, points, condensor, air filter, and fuel filter. And, you need to bear in mind that–unlike modern cars–this tune-up will need to be done around every 10k to 12k miles if you want to keep the car running at its optimum.
Keeping the tires properly inflated will help a bit. Replacing non-radial tires with radial tires will also help a bit.
The biggest problem that you are likely to run into is carburetor adjustment, if that becomes necessary. Any of the younger mechanics in the shop where you take the car are unlikely to have every worked on a carburetor. If it ever gets to the point where adjustment, or rebuilding, or replacement of the carburetor is needed, you will need to seek a mechanic who is over the age of 50.
As to the radiator, you just might have to replace it if simply doing things like soldering a top seam do not do the trick. Radiators have a finite life span, and this is shortened drastically if the previous owner(s) did not change the coolant frequently.
Don’t ignore the radiator leak as it can suddenly worsen, leading to overheating. If your engine overheats, it may sustain some serious damage.