Schwinn installed brick tread tires on a few million of their bikes from the 50's to the 90's and I've never heard of anyone suing over tire traction issues. Having a big aggressive tread isn't always going to keep you from going down, and if you make a sharp turn on a sand dusted asphalt street or a wet street you're at risk. I can say that from personal experience. As a kid I rode a 64 Varsity, 1-1/4" tires, in places you wouldn't image and never had an issue and there is basically no tread at all, very similar to a cheater slick and SKINNY. I rode that bike in rain storms, down dirt and gravel canal roads, thru the desert paths in Apache Junction, BMX'd in the old Hohokam canals and ditches and never went down. Came close a few times but never biffed it. When I made a right turn after going thru a very small spot of water in a gutter on my Taco mini bike, with knobby tires, I went down like a lead turd and slid across the asphalt with the mini bike on top of me. Like an idiot, I was at full throttle and didn't think that little bit of water on 150 degree asphalt would be a problem. A few years later in life I made a right hand turn, at night, on a sand dusted asphalt street with my Honda Hog and I went down real quick and hard. I'm probably your age and have no reservations using these brick tread tires on my rider. My biggest fear is stepping on that dropped bar of soap in the shower and then falling cracking my head open on the toilet.
That Jaguar was factory issued with Westwind whitewall brick treads and a WW set of these tires would make a new buyer/owner happy.