With some work it would be possible. I think it'd be easier if you started with a truck that didn't have knee-knocker windows like a 64-66. Your 61 body sat on more of an X-shaped frame, as opposed to the later years having a ladder-style frame. I swapped beds on my 65 with a 62 and there was a few minor issues with it fitting. I imagine you'd run into the same thing. Not a deal breaker, but it wouldn't just bolt right on.
It's hard to see because of the angle, but if you notice the 65 (black in background) has narrow frame that remains the same width through to the cab, where the 62 (blue foreground) has a wider frame that tapers in towards the cab.