How can i make single wall rooms a double wall with loosing minimal space.?

The house is an old single wall tongue and groove plantation style redwood home in Hawaii. The previous owner damaged many of the interior walls to where i can t just paint them. I need to make double walls in many areas to cover up holes but am wondering if i could use 2x2s instead of the regular 2x4 double wall framing style to loose less area since the rooms are not that big, especially the bathroom. Doing it myself on a budget so any pointers welcome.