During a non charged timeout such as the OP suggests for a team manager to report substitutions, there aren't restrictions on player activities.
If the player wants to throw to stay warm, do pushups, run to the centerfield fence and back, gather with his teammates and discuss who is taking whom to the prom, or most anything else, it is legal. As long as they are ready to play after the timeout has concluded.
Playing catch with the 3rd baseman is not only legal, but very traditional.
Of course, when I say anything... that does not include things that are specifically prohibited: unsporting conduct, doctoring the baseball, etc.
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