The proper way to test any "cured" paint coating is to use a :"solvent test".
Firstly clean the surface (a test area) with detergent and warm water and allow to dry.
Step 1. get a rag and saturate it with meths and hold onto the surface for 60 seconds.
If the coating softens and transfers to the cloth then it is a water based Acrylic or vinyl. (Highly unlikley, But possible). if it does'nt, it is either Enamel, Epoxy(doub't it as Epoxy's have no UV resistance but have been used on Steel boats for durability)?, Chlorinated rubber, Acrylic Lacquer (auto paint)or urethane.
Step 2. Obtain some tolulene or Xylol (some Antifouling thinner. ASee Date sheet or label for contents)and repeat the above. If the coating softens very easily then it is either Chlorinated Rubber, or Acrylic lacquer.If it softens just slightly then it is Enamel (1 pack) If it does'nt soften it is a polyurethane (acrylic Urethane, Aliphatic (linea) Urethane or urethane Enamel.
Step 3. Obtain some Methyl Ethyl Ketone (MEK) (Urethane spraying thinners) and repaet the above test but hold on surface for 1-2 minutes. if there is any signs of softening then it may be a acrylic Urethane. if not it is either one of the other two urethanes ofr a epoxy.
Now for the bad news...
If the coating is single pack Acrylic, or Chlorinated Rubber (which i doubt) and in stabe (non flakeing) condition then clean down and re coat with Acrylic / Chlorinated Rubber respectivley. (no sanding nor undercoat)
If the coating is Enamel (in stable condition) . then abrasion followed by a single pack enamel undecoat will be required before top coating.
if the coating is any type Urethane then sanding or (SS wire brushing if a non skid pattern) abrasion will be required prior to undercoating and top coating with 2 pack urethane products.
2 pack will give 2-3 times better durability for the same effort and a little more cost.
If you are a Brush and roller person then single pack is easiest. Thier are new 2 pack urethanes that brush and Roll easily.