I don't really blog much at all anymore so I didn't see this. Sorry for the wait... although I'm sure it didn't stop you from figuring something out.
The wet/dry is great and I wouldn't discourage using one, but the skimmer is more important. The skimmer IS your filtration. Otherwise, you should just do regular water changes, in any scenario. Water changes can negate the need for heavy duty filtration systems. I've seen some really gorgeous self-sustaining reef tanks that have NO filtration systems. That said, you don't need all the bells and whistles a reef tank typically requires to keep an octopus.
Get a good skimmer. Seal the lid of your tank. Feed the octopus thawed, raw shrimp bought from the supermarket. Easy as that. I swear. The hard part is finding an octopus that isn't already "old". Buying online from a reputable store that will offer a guarantee of sorts is preferable. Honestly, I never had much luck with the octopuses I got from this website, and after discussing it with many others on TONMO, it seemed that it's likely the animals they were receiving were likely caught in a manner that was ultimately fatal to most of the animals. That's a real shame, because O. hummelincki makes a great, fun pet. I haven't ordered one from here in a while though, that might have changed.