To get a single EXE file without DLL dependencies, you need static libraries. To know more about it, please check the wxWidgets documentation on how to create them (also the compiler documentation if you want to create your own).
You may need to modify the current project settings to use the static version of the libraries once you get them. Please refer to the wxWidgets documentation to see what needs to be changed.
If you need more help about it, please ask in the wxWidgets forums.