Well seeing as GM made all divisions share cowl, and front door stampings as well as green house in 1959 to speed up the change over to the all "new" 1959's, and 1960 is just a facelift on 1959, I would say yes.
The convertible top mechanism I believe is the same across all divisions, so the panels should all fit in the same way.
I can't say for certain for 1960, but what I have compared was '59 Impala 2dr HT to '59 Cadillac 2dr HT, and the panels will all interchange, so it stands to reason the convertible will as well. One of the neat lesser known facts about the 1959 models.