In general, yes, the tricky part is to select which one is used.
CodeBlocks, at least when building with autotools, uses the wx-config script. Depending on how you install the wxWidgets versions installation source and/or order determine which one will be used by default: the one from /usr/bin or /usr/local/bin and to what real version the symlink points.
The CodeBlocks autotools don't supply the requested version to the wx-config script but you can tell it which script to use. In my case, my selfbuild wx-master installs wx-config into /usr/local/bin which points to /usr/local/lib64/wx/config/gtk3-unicode-3.1. If i want to make sure that CodeBlocks uses this version i would execute ./configure --with-wx-config=/usr/local/lib64/wx/config/gtk3-unicode-3.1
I don't use Linux Mint, i don't know what packages they offer, but you can always compile from source. You might need to figure out which packages you need to install to be able to compile, since it offers wxWidgets 3.0 a good start would be to install the dev-packages of the libraries this package depends on.