The specialty tickets you have will not be stripped away from you if you deactivate the character holding them. Shinies aren't restricted by Rank, like the other specialty tickets are, so don't worry about losing it. Make a leaving post for the character you wish to switch out and ask for Victini to approve your new character. Since it's a special case of switching, your spot will be held. Note that you cannot post for your new character if Victini has not approved it.
I would suggest keeping your current character there, if only on Idle, until your new character is approved, to prevent confusion as far as your spot on the team is concerned.