I tried, e.g., :exe "norm \<C-w>s" to split window, but failed.
:exe "norm \<C-w>s"
By the way, vifm --remote +$'normal \x17s' works.
vifm --remote +$'normal \x17s'
This comes up rarely enough that I constantly postpone implementing it... There is no way as of now (really need to add at least \xXX, although expanding keys should be equally easy) other than mapping that to an alphanumeric sequence and using it as an alias, for example:
\xXX
nnoremap _cw <c-w> execute 'norm _cws'
Update. "\<key>" sequences were implemented, so :exe "norm \<C-w>s" will work in v0.15.
"\<key>"
Not a direct answer to your question, but you might not need the Ctrl key if you use :wincmd instead.
:wincmd
Give execute 'wincmd s' a try.
execute 'wincmd s'