I am fortunate I only had one small "wet" area...below/around the port bow stanchion, the aft end of it is into cored deck.
If you only have a little bit (but sounds like you don't) then the injection method is good...the key to keeping a small area small is to dry it out well before injecting....I dried mine out for a week with heat below it and a container over top to ensure no water nor condensation got in. I dug out the wet stuff with a dental pick...like I said, I was lucky...
We have rain for weeks at a time here, 27 days straight last month, so the key here is to keep the boat as dry as reasonably possible if not using her, many blue tarps in marinas here full time.
Also, if you can, check your boat weekly for any water drips or leaks, find the source, (sometimes tough) and then fix that source, then make sure it stays fixed.
Here's what can happen with water: My mast has skookum new inner wiring, (done by old owner just before I bought her in 2004) but where the wires came into the boat, water was sneakly running above the mast support beam, along the wiring for the head, and along the liner ledge under the chainplates, and down the bulkhead base, and ended up both under the teak & holly sole skin as well as under the sole liner to rest on top of the holding tank....would then slosh around when heeled inside and outside the liner!
I found it by my curious nature: why was water there and where was it coming from. I would mop it up daily, and after only a few months of ownership I figured it out...So, imagine what that water would do if left unchecked for years.....Í am of the belief that no, our boats should not leak, and if it does, I will find it! ;-)
Ok, sorry to always talk so much about myself and my boat! ;-)