I cannot find a definitive answer to the question of whether we can offer arbitration to a player's who option we declined, but anyways... per MLBTradeRumors:
Type A (Compensation: The 1st round pick of team who signs the player (2nd round if in top 1/2 of round 1), Supplemental pick after round 1)
Type B (Compensation: Supplemental pick after round 1)
None (Compensation: None)
I very much doubt a team is going to give up it's pick to sign Rhodes or Hernandez, which makes me suspect we'll bring them back.