I don't know the SECOND WAVE album well enough to say, but The Beach Boys have always sounded fine doing Jan & Dean tunes and vice versa.
In the 1980s, "Surf City" and "The Little Old Lady from Pasadena" were always part of the respective surf and car medleys in a Beach Boys' show. I used to wonder how many in the audience knew they were Jan & Dean numbers. BTW- The Beach Boys performed no Jan & Dean material at the C50 show I attended in 2012 or Mike Love's Beach Boys Band gig I saw in 2014.
Jan & Dean performed tons of Beach Boys' material at their shows 1978-onward. Probably too much, but I understand Dean wanted to please the crowd. Regardless, I'd rather hear Jan & Dean do "The Anaheim Sewing Circle, etc" than say "Help Me Rhonda" at one of their own shows.
But again, the summer fair circuit both bands played wasn't geared toward deeper cuts or "fanboy" favorites.