My recollection of 1966 and what I was told of 1961 are that both clubs changed jerseys because of a clash. In those days very few people bought replica shirts and even fewer second choice shirts ; I say second choice because I recall that in those days in the event of a colour clash the home team changed strip. Both sets of supporters at Wembley would have had red/cherry and white scarves hats etc and it was felt unfair to make either team change colours.
If I remember the Red Vee shirt became associated with big matches and in 1965-66 as many replica shirts with the Vee (worn only once that season - at Wembley) were bought as those with the band.
I certainly remember one big match between Wigan and Saints for which both were allowed to keep their traditional shirts albeit with minor changes. I cannot remember whether Wigan had narrower or broader hoops than usual and whether Saints had a broader or narrower Vee than usual. Again I'm not sure whether by that time Saints had adopted the Vee for good or whether it was still their "big game" shirt.