I'm not sure why you would want to use Betadine.
It only slowly releases Iodine and is probably more expensive.
The polyvinylpyrrolidone it contains is a positively charged polymer that dissolves in water or alcohol but not in ether.
Therefore it may gel up your collodion.
It may even react with the Iodine released during the aging process thus inhibiting the collodion ripening process.
As a positively charged molecule it can form salts with any negatively charged molecules such as Iodides or Bromides which may precipitate from your collodion.