For Select mode, if that is really what you mean, these mappings would work:
vnoremap <S-Up> gk
vnoremap <S-Down> gj
imap <S-Up> <Esc>gh<S-Up>
imap <S-Down> <Esc><Right>gh<S-Down>
nmap <S-Up> gh<S-Up>
nmap <S-Down> gh<S-Down>
Note the gh
command (Select mode) instead of v
(Visual mode).
But be warned that – and this is an assumption on my part – the general populace of Vim users shun Select mode, seeing as it runs counter to the Vim way.
Visual mode is much more powerful, since in addition to replacing text, you can also yank it into a register, make it uppercase or lowercase, change the extent of the Visual selection, etc. etc. Have a look at :h vim-modes
.