Thanks for your interest doubletruck.
Not completely sure what you mean by only unclaimed players being drafted in '62 so I'll just give you the rundown of the league so far.
This is a single season progressive and we started in '61. Only players that had a WIS season in '61 were drafted for the first season. Everyone drafted their usual 25 man roster and the remaining players left at the end of the Initial Draft were randomly assigned. The randomly assigned players were the scraps and some owners didn't bother to roster them to AAA. "talisman25" is the current owner of this team and after the draft realized he didn't draft a 1Bman. I swapped him Bob Boyd-1B for one of his AAA players so he could fill his 1B spot when he put his team together. Not a big deal as neither player made a difference either way.
You can keep any and/or all active players from the roster listed above that have a season in '62 for the 2nd season of the league. Any Cuts you make will go into the draft pool for the '62 draft. The pool will consist of all players Cut from the 16 teams in the league, + veteran players that were on IR for the '61 season, + rookies from 1962.
The roster above has 2 players retiring leaving 24 available to keep. You could keep them all and still draft up to 11 more players, filling your AAA. Or you could just draft 1 player to fill your 25 man roster and decide not to draft anymore players. It is up to you how many picks you want to make in the draft. You just have to have a minimum of 25 and a maximum of 35. All players in AAA can be used up to the 120 day TD. In '62 there were 20 teams in RealLife MLB. With the league being 16 teams that gives us extra players that I felt would make the use of AAA a good thing. How you use your AAA is up to you.