How much risk are you willing to accept? There are many thousands of people out there who have no knowledge of actual tire life expectancy happily motoring along on tires far older than yours. When I bought my TT in 2011, it had the original Canadian GY Marathons from 1994. I hauled it 75 miles home and one 320 mile round trip before I got the new tires on. And I lived to tell about! Was it a risk? Sure. Big risk? Not really. Most tires will last far longer than the recommended life. Some won't.
When I was shopping for my trailer, I looked at several similar vintage units where the owner said the tires were in great shape. When I asked how old they were, they were original equipment. Most of the these people thought I was full of sh*t when I told them trailer tires are only good for a few years no matter what they look like. So you know there's lots of them out there on the road.