Writing about summer camp in the nostalgia section of course brought to mind the actual camps I went to, and those my children went to (a total of at least 11). There's a youtube page of summer camp songs, of course.
Wishy Washy Washer Woman, Little Bunny Foo Foo, In a Cabin, Boom Chicka Boom - those are here. The site does seem to lean to more recent decades, though.
To get back to my earliest era, there would have to be "We are the Havey's girls. We wear our hair in curls..." "I'm Mi-Te-Na born and Mi-Te-Na bred..." "Three Jolly Fishermen," or "Oh Mona!" Gad, camp songs are awful, but we loved them anyway.
Nope, no video. Too many to choose from.