Gary, there is no paint on an O'day sailboat unless it has been added by an owner, and that is highly unlikely. The cosmetic surface you see is gel-coat, a non-reinforced, colored resin sprayed into the mold before the layup of glass and resin begins.
The work you want to do is a complex subject and volumes have been written on it. Not knowing your specific problem/situation, it is hard to answer. You need to research it a little to know the possibilities.
All that aside, I saw a mid 1970s O'day 23 on Saturday that had the topsides coated (painted, to some) with Imron in the early 80s. It still looks fantastic after 30 years! Amazing! Imron is, or was, the automotive equivalent of the two-part polyurethane coatings such as Awlgrip or Interthane used in some boat refurbishing. Not really a DIY job for most, however.