275/60/15’s are supposed to have an 11” wide section width and a 8.9” wide tread width. That’s on an 8” wide rim. Your valiant probably only has about 11” from the springs to the quarters. Recommended rim width is 7.5”-9.5”, and even on a 7.5” wide rim those tires will be a little squeezed. But hey, if you can find a tire shop that will mount them, have at it.
It’s your car, so, do what you like. People certainly have done it, and I suppose if you can’t tell the difference in handling you probably aren’t driving hard enough for it to be a problem.