For regular cleaning I have a steamer and I use F10 disinfectant which is safe once it dries. I worry about fumes too so any pet stuff that gets bleached gets hosed and left in the sun.
For the big branches branches I put them in the
bath tub, and scrubbed and marinated them, basically. After that it was out to be yard for a few minute hose off. Then it got left out in the sun for the chlorine to break down, for a couple days.
When I use hot water and something dosnt fit in the pot I'll boil up water in a big stock pot and slowly pour it over. I wish I had a pot that big! Hehe. (I also do this to sterilize my dubia frass before composting it)
Neither method will reach too deep into the wood, but It's better than nothing. It's not as thorough as baking of course.
I will say in I've not had a problem with anything growing out of my branches, even the ones that just got rinsed with hose water and scrubbed. Any plant matter (moss, lichens etc) dies very quickly and I've not really had uninvited bugs appear either.