Vimwiki checks if mappings for its commands are set.
If not, it uses 'default' bindings.
So if there is no mapping to <Plug>VimwikiDiaryPrevDay then <C-Up> is bind to it. The same goes with <C-Down> and <Plug>VimwikiDiaryNextDay.
Add the following to your vimrc:
nmap <S-Up> <Plug>VimwikiDiaryPrevDay
nmap <S-Down> <Plug>VimwikiDiaryNextDay
Change <S-Up> and <S-Down> to whatever you want.
Maxim.