If the OP signed the guy this season (and he has a top 16 pick), he'd lose only his second round pick this year.
If the player turns into a Type B for next season (or beyond), and someone else signs him, the OP would get a supplemental round pick for that season, which would almost certainly (barring a truly obscene unbalance in FA classes) be earlier than the Round 2 pick he'd give up for signing the type A pick this year.