Good questions, Nancy. This is exactly what our forum is for!
The two part sticks are thickened epoxy – a resin stick and a hardener/catalyst stick. The ‘thickened’ part means it is not runny (normally, most epoxies one buys are like honey) . Tiny bits of powdered glass, plastic or minerals like talc do this thickening job.
This stuff is very practical to carry for a number of potential repairs because it has good shelf life, handles easily but hardens quite quickly (varies by type) . It doesn’t contaminate your stuff and food with nasty fumes (unlike other resins) and it works on most surfaces.
However, it is really only a stop-gap because your boat is not made of this – the most expensive type of resin.Iinstead your boat is made of a vinylester resin (kevlar reinforced boats) or a polyester resin (most glass reinforced boats). Only my Pygmy or another ‘wooden’ kayak will be made of epoxy resin (because those other resins won’t bond as well to wood).
What this means, is that the stick repair is temporary – grind it out later and fix properly (unless it is so small that it doesn’t really matter).
I would try chandlers like Steveston Hardware or West Marine or Martin Marine. They might have it a Home Despot too. They make some that it specifically for marine or underwater use, but I doubt that matters for a temporary repair.
Use rubber gloves. Those chemicals are not benign…
Plumbers putty will plug small holes but will not harden and has no real strength- more like chewing gum (another time-honoured multi-purpose sealant). Another type of material that works well is a sealant/adhesive like 3M 5200 or Sika-Flex. These don;t have great shelf life and are messier to use but for some repair are better because they are flexible as well as waterproof e.g. for bulkhead sealing (a common need in kayaks, especially those reinforced with kevlar, because they flex more).
Sorry to be so long-winded.