Well I can't open that link, but I'm in a similar situation of having big equity and wanting to trade down. I too have little experience of moving, but I think you will only be cash buyers if you have the actual cash from the sale of your house, not the eventual sale, if you get my drift. Hard cash will be needed at some point, not promises.
As for buying though, with no mortgage to apply for or get, it will cut down the time a bit simply because you have no reason to wait like most.
I'm going to sell mine, store stuff, and then rent a place while I look.