Your example is trying to mimic popup menu by popup window, it's complicate, I changed it to use arrow keys to scroll popup window in normal mode, it's only purpose is to show you how to change cursor in popup window:
noremap <buffer> <down> :call Omni_cursor(1)<CR>
noremap <buffer> <up> :call Omni_cursor(0)<CR>
The style of these two settings is defined by the CursorLine and CursorColumn highlight groups.
If I query these two on my Vim, I get:
CursorColumn xxx term=reverse ctermbg=242 guibg=Grey40
CursorLine xxx term=underline cterm=underline
So what we want to do is make CursorLine look more ...
I actually went with coloring the background of the line number. This way you're not interfering with syntax colors or underscores.
So basically I have this (for light background terminal)
highlight CursorLineNr ctermfg=white guifg=white ctermbg=darkgrey guibg=darkgrey cterm=bold gui=bold