If you're worried about urethane dissolving, use the same material as the resin in the hot tub - i.e. polyester resin. Marine supply houses have good resin, appropriate thickeners, as well as agents for secondary bonding (new FRP to old FRP). Below is a 'finishing' resin that cures with a dry surface. 'Laminating' resins cure a leave a tacky surface.
http://fiberglasssupplydepot.com/Premium-Polyester-Resin.html
Here's some glass micro-bubbles that are mixed in to the resin to thicken it
http://fiberglasssupplydepot.com/GLASS-BUBBLES.html
Or just get one batch of their 'fairing' compounds (pre-thickened).
If you're worried about the chlorine content and heat of the hot tub, then use a premium vinyl ester resin instead of the polyester above. And a quart of resin will be way more than you need for some treads and plenty to practice with.
Scuff the surface, wipe with acetone, then lay out a 'tread' with painters tape. Catalyze a batch of resin a bit light (more pot life) and mix in some glass bubbles until the texture is like sour cream. Spread inside the tape area and roll with a loop paint roller to add surface texture. Peel up the tape before it's rock hard for a clean edge that will look factory. If it's not thick enough, add a second coat. Too thick or sharp - knock down the pointy bits with a block sander.
The resulting treads will be hard, grippy, and will never peel up or dissolve before the hot tub itself disintegrates. You'll have maybe $30-40 in materials and a couple hours of time.
If you want to get swank, you can pigment the resin (before catalyzing) to match or contrast the existing color.