No, they cannot.
You were unfortunately given incorrect information, because RapidWeaver, Sandbox, Coda and Freeway Pro do not have import facilities to import html files into their sites and will definitely not be able to open anything that was created by iWeb - they will only be able to open what has been created using them.
The only one of those that might be able to import html is Coda, but other than that the other apps cannot do that as they need to be html editors to do that and they are not.
Flux V has that capability, but has a massive learning curve and so does Dreamweaver, which is worse than Flux.
I would look around for an app that you like and then start again from scratch. That is the best way and also take a look at EverWeb along with the rest - this is probably a better and easier alternative to learn if you are coming from iWeb, as it is very much like iWeb.