Well let's see. My '49 had old cracked tires on it when I bought it, and I drove it for 10 years (about 5000 miles,) including a 550 mile, 12 hour trip from FL to NC with no problems (I did have a good spare and can of fix-a-flat!)
My current '40 has ancient WW Universals on it, and I plan to replace those when $ permits. But for now, I'm driving on them and I even got up to 50 MPH for the first time last week
Seems those old tires don't usually come apart like modern radials. So, I would say, just be aware something might let go and drive accordingly. Be safe and have fun!
Edit: I should add, I would not drive radials that are cracked or over 10 years old, period.
