RE: Ben Pearson Puma 62" Recurve
Again, it depends on condition and how well the bow was stored for all those years. I've shot some 50's bows in the past few years that still shot great. Didn't blow up even at 32" draw. I've got a 60's Pearson Colt that I've been shooting for dang near six months. It stacks like a ton of bricks at my draw length, but it doesn't complain at all.
There are few places where a 35 pound bow is legal for deer hunting. Check your game laws. Not all game wardens are knowledgeable about archery. Even if you draw a couple inches longer and get up to a legal draw weight, you might have to explain the draw force curve of recurve bows to the judge.
Even if it is a legal draw weight where you live, I would hesitate to shoot a deer with it beyond 15 yards or so. It'd be fine for small game though.